144:@0.032380:0.974518:0.061577:0.974518:0.061577:0.956590:0.032380:0.956590:0.000000:0.000000:0.000000
Funciones:@0.073089:0.043661:0.163813:0.043661:0.163813:0.024916:0.073089:0.024916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
8.2 Propiedades de los logaritmos:@0.293660:0.136836:0.559733:0.136836:0.559733:0.119889:0.293660:0.119889:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Teorema. :@0.293660:0.164198:0.364469:0.164198:0.364469:0.147515:0.293660:0.147515:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sea   > 0,   ≠ 1 base de la función logarítmica :@0.364712:0.164198:0.705027:0.164198:0.705027:0.147764:0.364712:0.147764:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.394661:0.164198:0.403920:0.164198:0.403920:0.147792:0.394661:0.147792:0.000000
a:@0.439593:0.164198:0.448852:0.164198:0.448852:0.147792:0.439593:0.147792:0.000000
Log:@0.705044:0.164198:0.730361:0.164198:0.730361:0.147792:0.705044:0.147792:0.000000:0.000000:0.000000
a:@0.730340:0.167372:0.735738:0.167372:0.735738:0.157807:0.730340:0.157807:0.000000
. Se verifican las siguientes :@0.735700:0.164199:0.931082:0.164199:0.931082:0.147766:0.735700:0.147766:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
propiedades.:@0.293668:0.180841:0.388138:0.180841:0.388138:0.164407:0.293668:0.164407:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
i. :@0.293660:0.208204:0.305533:0.208204:0.305533:0.191535:0.293660:0.191535:0.000000:0.000000:0.000000
log αβ:@0.323858:0.208204:0.375387:0.208204:0.375387:0.191798:0.323858:0.191798:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.345915:0.211377:0.351313:0.211377:0.351313:0.201812:0.345915:0.201812:0.000000
(:@0.351273:0.208204:0.356501:0.208204:0.356501:0.191535:0.351273:0.191535:0.000000
) = :@0.375331:0.208204:0.399114:0.208204:0.399114:0.191535:0.375331:0.191535:0.000000:0.000000:0.000000:0.000000
log α:@0.399022:0.208204:0.441137:0.208204:0.441137:0.191798:0.399022:0.191798:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.421070:0.211377:0.426468:0.211377:0.426468:0.201812:0.421070:0.201812:0.000000
( ) + :@0.426430:0.208204:0.464846:0.208204:0.464846:0.191535:0.426430:0.191535:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
log β:@0.464754:0.208204:0.506806:0.208204:0.506806:0.191798:0.464754:0.191798:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.486812:0.211377:0.492210:0.211377:0.492210:0.201812:0.486812:0.201812:0.000000
( ), :@0.492172:0.208204:0.519529:0.208204:0.519529:0.191535:0.492172:0.191535:0.000000:0.000000:0.000000:0.000000:0.000000
α β:@0.588119:0.208204:0.614644:0.208204:0.614644:0.191798:0.588119:0.191798:0.000000:0.000000:0.000000
,     :@0.597599:0.208204:0.637543:0.208204:0.637543:0.191535:0.597599:0.191535:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∈ ℝ:@0.618399:0.208787:0.650759:0.208787:0.650759:0.191133:0.618399:0.191133:0.000000:0.000000:0.000000
+:@0.650665:0.200880:0.657061:0.200880:0.657061:0.191161:0.650665:0.191161:0.000000
.:@0.657016:0.208204:0.660826:0.208204:0.660826:0.191535:0.657016:0.191535:0.000000
ii. :@0.293660:0.235994:0.309766:0.235994:0.309766:0.219324:0.293660:0.219324:0.000000:0.000000:0.000000:0.000000
log:@0.323858:0.235994:0.345965:0.235994:0.345965:0.219588:0.323858:0.219588:0.000000:0.000000:0.000000
a:@0.345915:0.239166:0.351313:0.239166:0.351313:0.229601:0.345915:0.229601:0.000000
 :@0.351273:0.235994:0.355175:0.235994:0.355175:0.219324:0.351273:0.219324:0.000000
α:@0.362214:0.229599:0.372006:0.229599:0.372006:0.213166:0.362214:0.213166:0.000000
β:@0.362214:0.243468:0.372209:0.243468:0.372209:0.227034:0.362214:0.227034:0.000000
       = :@0.381009:0.235994:0.422610:0.235994:0.422610:0.219324:0.381009:0.219324:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
log α log β:@0.422496:0.235994:0.520720:0.235994:0.520720:0.219588:0.422496:0.219588:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.444551:0.239166:0.449949:0.239166:0.449949:0.229601:0.444551:0.229601:0.000000
   – :@0.449911:0.235994:0.480080:0.235994:0.480080:0.219324:0.449911:0.219324:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.502052:0.239166:0.507450:0.239166:0.507450:0.229601:0.502052:0.229601:0.000000
  , :@0.507412:0.235994:0.528289:0.235994:0.528289:0.219324:0.507412:0.219324:0.000000:0.000000:0.000000:0.000000
α β:@0.588119:0.235994:0.614644:0.235994:0.614644:0.219588:0.588119:0.219588:0.000000:0.000000:0.000000
,     :@0.597599:0.235994:0.637543:0.235994:0.637543:0.219324:0.597599:0.219324:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∈ ℝ:@0.618399:0.236576:0.650759:0.236576:0.650759:0.218922:0.618399:0.218922:0.000000:0.000000:0.000000
+:@0.650665:0.228669:0.657061:0.228669:0.657061:0.218951:0.650665:0.218951:0.000000
.:@0.657016:0.235994:0.660826:0.235994:0.660826:0.219324:0.657016:0.219324:0.000000
iii. :@0.293660:0.272397:0.314000:0.272397:0.314000:0.255727:0.293660:0.255727:0.000000:0.000000:0.000000:0.000000:0.000000
log α :@0.323858:0.272397:0.369220:0.272397:0.369220:0.255990:0.323858:0.255990:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.345915:0.275569:0.351313:0.275569:0.351313:0.266004:0.345915:0.266004:0.000000
(:@0.351273:0.272397:0.356501:0.272397:0.356501:0.255727:0.351273:0.255727:0.000000
m:@0.369317:0.261010:0.378485:0.261010:0.378485:0.250718:0.369317:0.250718:0.000000
n:@0.370922:0.270840:0.376880:0.270840:0.376880:0.260548:0.370922:0.260548:0.000000
) =    :@0.378578:0.272397:0.427749:0.272395:0.427749:0.255726:0.378578:0.255727:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
m:@0.403874:0.263464:0.418490:0.263464:0.418490:0.247058:0.403874:0.247058:0.000000
n:@0.406433:0.279856:0.415931:0.279856:0.415931:0.263450:0.406433:0.263450:0.000000
log α:@0.427675:0.272395:0.469787:0.272397:0.469787:0.255990:0.427675:0.255989:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.449722:0.275569:0.455120:0.275569:0.455120:0.266004:0.449722:0.266004:0.000000
( ), :@0.455080:0.272397:0.482510:0.272397:0.482510:0.255727:0.455080:0.255727:0.000000:0.000000:0.000000:0.000000:0.000000
α:@0.588121:0.272397:0.597674:0.272397:0.597674:0.255990:0.588121:0.255990:0.000000
   :@0.597601:0.272397:0.620573:0.272397:0.620573:0.255727:0.597601:0.255727:0.000000:0.000000:0.000000
∈ ℝ:@0.601429:0.272979:0.633789:0.272979:0.633789:0.255325:0.601429:0.255325:0.000000:0.000000:0.000000
+:@0.633696:0.265072:0.640092:0.265072:0.640092:0.255354:0.633696:0.255354:0.000000
, :@0.640046:0.272397:0.647685:0.272397:0.647685:0.255727:0.640046:0.255727:0.000000:0.000000
m, n:@0.659260:0.272397:0.689798:0.272397:0.689798:0.255990:0.659260:0.255990:0.000000:0.000000:0.000000:0.000000
     con   ≠ 0.:@0.689761:0.272397:0.801879:0.272397:0.801879:0.255727:0.689761:0.255727:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∈ ℤ:@0.693590:0.272979:0.724937:0.272979:0.724937:0.255325:0.693590:0.255325:0.000000:0.000000:0.000000
n:@0.760721:0.272397:0.770219:0.272397:0.770219:0.255990:0.760721:0.255990:0.000000
Demostración  Sean  ,     :@0.293674:0.310479:0.492858:0.310479:0.492858:0.294045:0.293674:0.294045:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
.:@0.396570:0.310479:0.400380:0.310479:0.400380:0.293809:0.396570:0.293809:0.000000
α β:@0.443674:0.310479:0.469702:0.310479:0.469702:0.294073:0.443674:0.294073:0.000000:0.000000:0.000000
∈ ℝ:@0.473586:0.311061:0.506075:0.311061:0.506075:0.293407:0.473586:0.293407:0.000000:0.000000:0.000000
+:@0.505969:0.303157:0.512365:0.303157:0.512365:0.293576:0.505969:0.293576:0.000000
.:@0.512318:0.310481:0.515521:0.310481:0.515521:0.294047:0.512318:0.294047:0.000000
i.  De la definición de las funciones :@0.293660:0.337843:0.567173:0.337843:0.567173:0.321174:0.293660:0.321174:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Exp:@0.566834:0.337843:0.591426:0.337843:0.591426:0.321437:0.566834:0.321437:0.000000:0.000000:0.000000
a:@0.591315:0.341015:0.596713:0.341015:0.596713:0.331451:0.591315:0.331451:0.000000
 y :@0.596644:0.337843:0.612437:0.337843:0.612437:0.321174:0.596644:0.321174:0.000000:0.000000:0.000000
Log:@0.611922:0.337843:0.637139:0.337843:0.637139:0.321437:0.611922:0.321437:0.000000:0.000000:0.000000
a:@0.637017:0.341015:0.642415:0.341015:0.642415:0.331451:0.637017:0.331451:0.000000
 se tienen las siguientes equivalencias::@0.642345:0.337843:0.926682:0.337843:0.926682:0.321174:0.642345:0.321174:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.323789:0.362709:0.333104:0.362709:0.333104:0.346303:0.323789:0.346303:0.000000
 = :@0.333030:0.362709:0.351916:0.362709:0.351916:0.346275:0.333030:0.346275:0.000000:0.000000:0.000000
log α:@0.351824:0.362709:0.393591:0.362705:0.393591:0.346299:0.351824:0.346303:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.373876:0.365877:0.379273:0.365877:0.379273:0.356313:0.373876:0.356313:0.000000
( ) :@0.379234:0.362705:0.402353:0.362705:0.402353:0.346271:0.379234:0.346271:0.000000:0.000000:0.000000:0.000000
⇔:@0.402261:0.362289:0.421442:0.362289:0.421442:0.345300:0.402261:0.345300:0.000000
   = :@0.421350:0.362705:0.453673:0.362705:0.453673:0.346271:0.421350:0.346271:0.000000:0.000000:0.000000:0.000000:0.000000
α:@0.425307:0.362705:0.434860:0.362705:0.434860:0.346299:0.425307:0.346299:0.000000
exp u:@0.453581:0.362705:0.497363:0.362705:0.497363:0.346299:0.453581:0.346299:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.477885:0.365877:0.483283:0.365877:0.483283:0.356313:0.477885:0.356313:0.000000
( ),:@0.483245:0.362705:0.505297:0.362705:0.505297:0.346271:0.483245:0.346271:0.000000:0.000000:0.000000:0.000000
v:@0.323783:0.390067:0.331514:0.390067:0.331514:0.373661:0.323783:0.373661:0.000000
 = :@0.331440:0.390067:0.350326:0.390067:0.350326:0.373633:0.331440:0.373633:0.000000:0.000000:0.000000
log β:@0.350234:0.390067:0.391936:0.390068:0.391936:0.373662:0.350234:0.373661:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.372293:0.393240:0.377690:0.393240:0.377690:0.383676:0.372293:0.383676:0.000000
( ) :@0.377652:0.390068:0.400698:0.390068:0.400698:0.373634:0.377652:0.373634:0.000000:0.000000:0.000000:0.000000
⇔:@0.400606:0.389652:0.419787:0.389652:0.419787:0.372664:0.400606:0.372664:0.000000
   = :@0.419695:0.390068:0.451944:0.390068:0.451944:0.373634:0.419695:0.373634:0.000000:0.000000:0.000000:0.000000:0.000000
β:@0.423652:0.390068:0.433132:0.390068:0.433132:0.373662:0.423652:0.373662:0.000000
exp v:@0.451852:0.390068:0.494050:0.390068:0.494050:0.373662:0.451852:0.373662:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.476155:0.393240:0.481553:0.393240:0.481553:0.383676:0.476155:0.383676:0.000000
( ).:@0.481515:0.390068:0.501983:0.390068:0.501983:0.373634:0.481515:0.373634:0.000000:0.000000:0.000000:0.000000
Luego,:@0.323783:0.417430:0.372715:0.417430:0.372715:0.400996:0.323783:0.400996:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 αβ:@0.372617:0.417430:0.394816:0.417430:0.394816:0.401024:0.372617:0.401024:0.000000:0.000000:0.000000
 = :@0.394761:0.417430:0.413647:0.417430:0.413647:0.400996:0.394761:0.400996:0.000000:0.000000:0.000000
exp u exp v:@0.413555:0.417430:0.504246:0.417431:0.504246:0.401025:0.413555:0.401024:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.437849:0.420604:0.443247:0.420604:0.443247:0.411039:0.437849:0.411039:0.000000
( ):@0.443207:0.417431:0.462130:0.417431:0.462130:0.400998:0.443207:0.400998:0.000000:0.000000:0.000000
a:@0.486351:0.420604:0.491748:0.420604:0.491748:0.411039:0.486351:0.411039:0.000000
( ) = :@0.491710:0.417431:0.527862:0.417431:0.527862:0.400998:0.491710:0.400998:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
exp u  v:@0.527752:0.417431:0.597291:0.417431:0.597291:0.401025:0.527752:0.401025:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.552061:0.420604:0.557459:0.420604:0.557459:0.411039:0.552061:0.411039:0.000000
( +  ),:@0.557421:0.417431:0.605225:0.417431:0.605225:0.400998:0.557421:0.400998:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de donde  +   = :@0.323778:0.444793:0.452555:0.444793:0.452555:0.428360:0.323778:0.428360:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u  v:@0.398677:0.444793:0.433743:0.444793:0.433743:0.428387:0.398677:0.428387:0.000000:0.000000:0.000000:0.000000
log αβ:@0.452463:0.444793:0.503640:0.444795:0.503640:0.428389:0.452463:0.428387:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.474516:0.447967:0.479914:0.447967:0.479914:0.438402:0.474516:0.438402:0.000000
(:@0.479876:0.444795:0.484754:0.444795:0.484754:0.428361:0.479876:0.428361:0.000000
) y consecuentemente,:@0.503585:0.444795:0.669467:0.444795:0.669467:0.428361:0.503585:0.428361:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
log αβ:@0.323783:0.472157:0.374958:0.472158:0.374958:0.455752:0.323783:0.455750:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.345836:0.475330:0.351234:0.475330:0.351234:0.465765:0.345836:0.465765:0.000000
(:@0.351195:0.472158:0.356072:0.472158:0.356072:0.455724:0.351195:0.455724:0.000000
) =  +   = :@0.374903:0.472158:0.452361:0.472158:0.452361:0.455724:0.374903:0.455724:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u  v:@0.398483:0.472158:0.433549:0.472158:0.433549:0.455752:0.398483:0.455752:0.000000:0.000000:0.000000:0.000000
log α:@0.452269:0.472158:0.494043:0.472158:0.494043:0.455752:0.452269:0.455752:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.474327:0.475330:0.479725:0.475330:0.479725:0.465765:0.474327:0.465765:0.000000
( ) + :@0.479686:0.472158:0.517660:0.472158:0.517660:0.455724:0.479686:0.455724:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
log β:@0.517549:0.472158:0.559257:0.472158:0.559257:0.455752:0.517549:0.455752:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.539615:0.475330:0.545012:0.475330:0.545012:0.465765:0.539615:0.465765:0.000000
( ).:@0.544973:0.472158:0.567190:0.472158:0.567190:0.455724:0.544973:0.455724:0.000000:0.000000:0.000000:0.000000
Observaciones:@0.293658:0.506662:0.401241:0.506662:0.401241:0.490228:0.293658:0.490228:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
::@0.401083:0.506662:0.404893:0.506662:0.404893:0.489992:0.401083:0.489992:0.000000
i.  Sean:@0.293660:0.534031:0.361562:0.534031:0.361562:0.517362:0.293660:0.517362:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 α, β γ:@0.361703:0.534031:0.407022:0.534031:0.407022:0.517625:0.361703:0.517625:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
,     :@0.391063:0.534031:0.430602:0.534031:0.430602:0.517362:0.391063:0.517362:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∈ ℝ:@0.411421:0.534614:0.444241:0.534614:0.444241:0.516960:0.411421:0.516960:0.000000:0.000000:0.000000
+:@0.444151:0.526707:0.450547:0.526707:0.450547:0.516988:0.444151:0.516988:0.000000
. Aplicando la propiedad asociativa del producto de números :@0.450627:0.534031:0.930587:0.534031:0.930587:0.517362:0.450627:0.517362:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
reales y la propiedad i) del teorema precedente, obtenemos::@0.323783:0.550673:0.789370:0.550673:0.789370:0.534004:0.323783:0.534004:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
log αβγ:@0.323783:0.575539:0.374900:0.575539:0.374900:0.559133:0.323783:0.559133:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.344730:0.575539:0.349608:0.575539:0.349608:0.559105:0.344730:0.559105:0.000000
) = :@0.374476:0.575539:0.397062:0.575539:0.397062:0.559105:0.374476:0.559105:0.000000:0.000000:0.000000:0.000000
log α βγ):@0.396583:0.575539:0.462831:0.575535:0.462831:0.559129:0.396583:0.559133:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.417541:0.578708:0.422939:0.578708:0.422939:0.569143:0.417541:0.569143:0.000000
( (:@0.422685:0.575535:0.441479:0.575535:0.441479:0.559101:0.422685:0.559101:0.000000:0.000000:0.000000
) = :@0.462776:0.575535:0.485362:0.575535:0.485362:0.559101:0.462776:0.559101:0.000000:0.000000:0.000000:0.000000
log α:@0.484883:0.575535:0.524974:0.575535:0.524974:0.559129:0.484883:0.559129:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.505839:0.578708:0.511237:0.578708:0.511237:0.569143:0.505839:0.569143:0.000000
( ) + :@0.510985:0.575535:0.547486:0.575535:0.547486:0.559101:0.510985:0.559101:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
log βγ:@0.547008:0.575535:0.594537:0.575535:0.594537:0.559129:0.547008:0.559129:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.567967:0.578708:0.573365:0.578708:0.573365:0.569143:0.567967:0.569143:0.000000
( ) = :@0.573111:0.575535:0.617067:0.575535:0.617067:0.559101:0.573111:0.559101:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
log α:@0.616589:0.575535:0.656671:0.575535:0.656671:0.559129:0.616589:0.559129:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.637538:0.578708:0.642936:0.578708:0.642936:0.569143:0.637538:0.569143:0.000000
( ) + :@0.642682:0.575535:0.679183:0.575535:0.679183:0.559101:0.642682:0.559101:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
log β:@0.678705:0.575535:0.718725:0.575535:0.718725:0.559129:0.678705:0.559129:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.699664:0.578708:0.705062:0.578708:0.705062:0.569143:0.699664:0.569143:0.000000
( ) + :@0.704810:0.575535:0.741238:0.575535:0.741238:0.559101:0.704810:0.559101:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
log γ:@0.740759:0.575535:0.778882:0.575535:0.778882:0.559129:0.740759:0.559129:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.761718:0.578708:0.767116:0.578708:0.767116:0.569143:0.761718:0.569143:0.000000
( ).:@0.766862:0.575535:0.786447:0.575535:0.786447:0.559101:0.766862:0.559101:0.000000:0.000000:0.000000:0.000000
De manera general, sean  , …     :@0.323781:0.602897:0.589612:0.602898:0.589612:0.586465:0.323781:0.586463:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
α:@0.507375:0.602897:0.516928:0.602897:0.516928:0.586491:0.507375:0.586491:0.000000
1:@0.516856:0.606071:0.522093:0.606071:0.522093:0.596490:0.516856:0.596490:0.000000
α:@0.551387:0.602898:0.560940:0.602898:0.560940:0.586492:0.551387:0.586492:0.000000
n:@0.560883:0.606071:0.566421:0.606071:0.566421:0.596506:0.560883:0.596506:0.000000
∈ ℝ:@0.570340:0.603481:0.602828:0.603481:0.602828:0.585827:0.570340:0.585827:0.000000:0.000000:0.000000
+:@0.602721:0.595574:0.609117:0.595574:0.609117:0.585993:0.602721:0.585993:0.000000
. Entonces, :@0.609070:0.602898:0.690270:0.602898:0.690270:0.586465:0.609070:0.586465:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
log α:@0.323776:0.623118:0.360186:0.623118:0.360186:0.606712:0.323776:0.606712:0.000000:0.000000:0.000000:0.000000:0.000000
( × … ×  ) = :@0.345828:0.623118:0.455207:0.623113:0.455207:0.606679:0.345828:0.606684:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.359752:0.626286:0.364989:0.626286:0.364989:0.616705:0.359752:0.616705:0.000000
α:@0.416905:0.623113:0.426458:0.623113:0.426458:0.606707:0.416905:0.606707:0.000000
n:@0.426018:0.626286:0.431556:0.626286:0.431556:0.616721:0.426018:0.616721:0.000000
log α:@0.455097:0.623113:0.495191:0.623113:0.495191:0.606707:0.455097:0.606707:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.476056:0.626286:0.481454:0.626286:0.481454:0.616721:0.476056:0.616721:0.000000
( )  + … + :@0.481202:0.623113:0.561787:0.623113:0.561787:0.606679:0.481202:0.606679:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.494749:0.626286:0.499986:0.626286:0.499986:0.616705:0.494749:0.616705:0.000000
log α:@0.561290:0.623113:0.601367:0.623113:0.601367:0.606707:0.561290:0.606707:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.582232:0.626286:0.587630:0.626286:0.587630:0.616721:0.582232:0.616721:0.000000
( ). :@0.587378:0.623113:0.618095:0.623113:0.618095:0.606679:0.587378:0.606679:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.600926:0.626286:0.606463:0.626286:0.606463:0.616721:0.600926:0.616721:0.000000
ii.  Sea     :@0.293660:0.650476:0.386811:0.650476:0.386811:0.633807:0.293660:0.633807:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
α:@0.354727:0.650476:0.364280:0.650476:0.364280:0.634070:0.354727:0.634070:0.000000
∈ ℝ:@0.367667:0.651059:0.400027:0.651059:0.400027:0.633405:0.367667:0.633405:0.000000:0.000000:0.000000
+:@0.399935:0.643152:0.406331:0.643152:0.406331:0.633433:0.399935:0.633433:0.000000
. Puesto que :@0.406286:0.650476:0.502896:0.650476:0.502896:0.633807:0.406286:0.633807:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
log:@0.502777:0.650476:0.524147:0.650476:0.524147:0.634070:0.502777:0.634070:0.000000:0.000000:0.000000
a:@0.523726:0.653649:0.529124:0.653649:0.529124:0.644084:0.523726:0.644084:0.000000
(1) = 0, se sigue que::@0.528870:0.650476:0.681886:0.650476:0.681886:0.633807:0.528870:0.633807:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
log:@0.491061:0.675592:0.513168:0.675592:0.513168:0.659186:0.491061:0.659186:0.000000:0.000000:0.000000
a:@0.513111:0.678759:0.518509:0.678759:0.518509:0.669194:0.513111:0.669194:0.000000
 :@0.518257:0.675587:0.522288:0.675587:0.522288:0.659153:0.518257:0.659153:0.000000
1:@0.530736:0.667225:0.539718:0.667225:0.539718:0.650792:0.530736:0.650792:0.000000
α:@0.530331:0.683867:0.540123:0.683867:0.540123:0.667433:0.530331:0.667433:0.000000
   = :@0.548115:0.675587:0.574916:0.675587:0.574916:0.659153:0.548115:0.659153:0.000000:0.000000:0.000000:0.000000:0.000000
log:@0.574807:0.675587:0.596178:0.675587:0.596178:0.659181:0.574807:0.659181:0.000000:0.000000:0.000000
a:@0.595758:0.678759:0.601156:0.678759:0.601156:0.669194:0.595758:0.669194:0.000000
(1) – :@0.600902:0.675587:0.636163:0.675587:0.636163:0.659153:0.600902:0.659153:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
log α:@0.636060:0.675587:0.676139:0.675587:0.676139:0.659181:0.636060:0.659181:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.657006:0.678759:0.662404:0.678759:0.662404:0.669194:0.657006:0.669194:0.000000
( ) = – :@0.662150:0.675587:0.712475:0.675587:0.712475:0.659153:0.662150:0.659153:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
log α:@0.712365:0.675587:0.752444:0.675587:0.752444:0.659181:0.712365:0.659181:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.733311:0.678759:0.738709:0.678759:0.738709:0.669194:0.733311:0.669194:0.000000
( ).:@0.738455:0.675587:0.759641:0.675587:0.759641:0.659153:0.738455:0.659153:0.000000:0.000000:0.000000:0.000000
iii.  Para   = 1 y :@0.293660:0.707845:0.419152:0.707845:0.419152:0.691176:0.293660:0.691176:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
m:@0.360360:0.707845:0.374975:0.707845:0.374975:0.691439:0.360360:0.691439:0.000000
n:@0.419042:0.707845:0.428540:0.707845:0.428540:0.691439:0.419042:0.691439:0.000000
 :@0.428483:0.711018:0.430415:0.711018:0.430415:0.701453:0.428483:0.701453:0.000000
∈ ℤ:@0.430377:0.708428:0.461725:0.708428:0.461725:0.690774:0.430377:0.690774:0.000000:0.000000:0.000000
   con   ≠ 0, :@0.445619:0.707845:0.542496:0.707845:0.542496:0.691176:0.445619:0.691176:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.497509:0.707845:0.507007:0.707845:0.507007:0.691439:0.497509:0.691439:0.000000
α :@0.542404:0.707845:0.555197:0.707845:0.555197:0.691439:0.542404:0.691439:0.000000:0.000000
∈ ℝ:@0.555142:0.708428:0.587502:0.708428:0.587502:0.690774:0.555142:0.690774:0.000000:0.000000:0.000000
 :@0.570383:0.707845:0.574285:0.707845:0.574285:0.691176:0.570383:0.691176:0.000000
+:@0.587393:0.700521:0.593789:0.700521:0.593789:0.690802:0.587393:0.690802:0.000000
, se tiene:     :@0.593744:0.707845:0.683148:0.707845:0.683148:0.691176:0.593744:0.691176:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
log α:@0.683000:0.707845:0.724775:0.707845:0.724775:0.691439:0.683000:0.691439:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.705059:0.711018:0.710457:0.711018:0.710457:0.701453:0.705059:0.701453:0.000000
(     ) =    :@0.710417:0.707845:0.789312:0.707845:0.789312:0.691411:0.710417:0.691411:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.729393:0.696458:0.735028:0.696458:0.735028:0.686150:0.729393:0.686150:0.000000
n:@0.729232:0.706288:0.735190:0.706288:0.735190:0.695997:0.729232:0.695997:0.000000
1:@0.769801:0.699483:0.778783:0.699483:0.778783:0.683049:0.769801:0.683049:0.000000
n:@0.769543:0.715875:0.779041:0.715875:0.779041:0.699469:0.769543:0.699469:0.000000
log α:@0.789220:0.707845:0.831000:0.707845:0.831000:0.691439:0.789220:0.691439:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.811284:0.711018:0.816682:0.711018:0.816682:0.701453:0.811284:0.701453:0.000000
( ).:@0.816642:0.707845:0.838933:0.707845:0.838933:0.691411:0.816642:0.691411:0.000000:0.000000:0.000000:0.000000
Para   = 1, :@0.323788:0.732711:0.402552:0.732711:0.402552:0.716277:0.323788:0.716277:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.358246:0.732711:0.367744:0.732711:0.367744:0.716305:0.358246:0.716305:0.000000
m:@0.402442:0.732711:0.417057:0.732711:0.417057:0.716305:0.402442:0.716305:0.000000
 :@0.416987:0.735880:0.418919:0.735880:0.418919:0.726315:0.416987:0.726315:0.000000
∈ ℤ ∈ ℝ:@0.418880:0.733290:0.500148:0.733290:0.500148:0.715635:0.418880:0.715635:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
       :@0.434121:0.732707:0.486931:0.732707:0.486931:0.716273:0.434121:0.716273:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
α:@0.454222:0.732707:0.463775:0.732707:0.463775:0.716301:0.454222:0.716301:0.000000
+:@0.500034:0.725383:0.506430:0.725383:0.506430:0.715802:0.500034:0.715802:0.000000
, se tiene :@0.506383:0.732707:0.573993:0.732707:0.573993:0.716273:0.506383:0.716273:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
log α:@0.573845:0.732707:0.615611:0.732707:0.615611:0.716301:0.573845:0.716301:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.595896:0.735880:0.601293:0.735880:0.601293:0.726315:0.595896:0.726315:0.000000
( ) = :@0.601254:0.732707:0.647710:0.732707:0.647710:0.716273:0.601254:0.716273:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
m:@0.615539:0.726643:0.624060:0.726643:0.624060:0.717079:0.615539:0.717079:0.000000
mlog α:@0.647600:0.732707:0.705218:0.732707:0.705218:0.716301:0.647600:0.716301:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.685502:0.735880:0.690900:0.735880:0.690900:0.726315:0.685502:0.726315:0.000000
( ).:@0.690860:0.732707:0.713151:0.732707:0.713151:0.716273:0.690860:0.716273:0.000000:0.000000:0.000000:0.000000
Ejemplo 2:@0.293650:0.767211:0.369433:0.767211:0.369433:0.750542:0.293650:0.750542:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1.  Se conoce que :@0.293660:0.794581:0.438651:0.794581:0.438651:0.777911:0.293660:0.777911:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
log:@0.438535:0.794581:0.460642:0.794581:0.460642:0.778175:0.438535:0.778175:0.000000:0.000000:0.000000
(2)   0,301 0, :@0.460587:0.794581:0.565196:0.794581:0.565196:0.777911:0.460587:0.777911:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
≃:@0.484075:0.795163:0.499408:0.795163:0.499408:0.777509:0.484075:0.777509:0.000000
log:@0.565085:0.794581:0.587192:0.794581:0.587192:0.778175:0.565085:0.778175:0.000000:0.000000:0.000000
(3)   0,477 1. Calcular el valor:@0.587137:0.794581:0.811363:0.794581:0.811363:0.777911:0.587137:0.777911:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
≃:@0.610625:0.795163:0.625958:0.795163:0.625958:0.777509:0.610625:0.777509:0.000000
aproximado de :@0.323784:0.819446:0.438191:0.819446:0.438191:0.803013:0.323784:0.803013:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
log:@0.438038:0.819446:0.460145:0.819446:0.460145:0.803040:0.438038:0.803040:0.000000:0.000000:0.000000
(  144 ) con cuatro cifras luego de la coma decimal.:@0.460090:0.819446:0.826770:0.819446:0.826770:0.803013:0.460090:0.803013:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Como 144 = 2  × 3 , entonces,:@0.323784:0.846808:0.542440:0.846806:0.542440:0.830372:0.323784:0.830375:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
4:@0.426850:0.840742:0.432087:0.840742:0.432087:0.831161:0.426850:0.831161:0.000000
2:@0.459732:0.840742:0.464969:0.840742:0.464969:0.831161:0.459732:0.831161:0.000000
log:@0.323774:0.874168:0.345882:0.874168:0.345882:0.857762:0.323774:0.857762:0.000000:0.000000:0.000000
(  144 ) = :@0.345826:0.874168:0.413495:0.874168:0.413495:0.857734:0.345826:0.857734:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
log:@0.413362:0.874168:0.435470:0.874168:0.435470:0.857762:0.413362:0.857762:0.000000:0.000000:0.000000
    2  × 3  = :@0.435414:0.874168:0.514877:0.874168:0.514877:0.857734:0.435414:0.857734:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
4:@0.457918:0.868104:0.463155:0.868104:0.463155:0.858523:0.457918:0.858523:0.000000
2:@0.490800:0.868104:0.496037:0.868104:0.496037:0.858523:0.490800:0.858523:0.000000
log:@0.514785:0.874168:0.536892:0.874168:0.536892:0.857762:0.514785:0.857762:0.000000:0.000000:0.000000
(2  × 3  ):@0.536837:0.874168:0.598580:0.874168:0.598580:0.857734:0.536837:0.857734:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
   :@0.550535:0.868104:0.557500:0.868104:0.557500:0.858523:0.550535:0.858523:0.000000:0.000000:0.000000
  :@0.585137:0.868104:0.589795:0.868104:0.589795:0.858523:0.585137:0.858523:0.000000:0.000000
=     :@0.323778:0.901530:0.354536:0.901530:0.354536:0.885096:0.323778:0.885096:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
log:@0.354426:0.901530:0.376533:0.901530:0.376533:0.885124:0.354426:0.885124:0.000000:0.000000:0.000000
(2) +      :@0.376478:0.901530:0.433669:0.901530:0.433669:0.885096:0.376478:0.885096:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
log:@0.433522:0.901530:0.455629:0.901530:0.455629:0.885124:0.433522:0.885124:0.000000:0.000000:0.000000
(3) =      × 0,301 0 +      × 0,477 1 = 0,431 64.:@0.455574:0.901530:0.764549:0.901530:0.764549:0.885096:0.455574:0.885096:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.467097:0.809023:0.472333:0.809023:0.472333:0.799442:0.467097:0.799442:0.000000
5:@0.350107:0.861965:0.355344:0.861965:0.355344:0.852384:0.350107:0.852384:0.000000
5:@0.437742:0.865628:0.442979:0.865628:0.442979:0.856047:0.437742:0.856047:0.000000
4:@0.551335:0.859436:0.556970:0.859436:0.556970:0.849128:0.551335:0.849128:0.000000
5:@0.551335:0.869266:0.556970:0.869266:0.556970:0.858958:0.551335:0.858958:0.000000
2:@0.585751:0.859436:0.591386:0.859436:0.591386:0.849128:0.585751:0.849128:0.000000
5:@0.585751:0.869266:0.591386:0.869266:0.591386:0.858958:0.585751:0.858958:0.000000
4:@0.339839:0.893332:0.348822:0.893332:0.348822:0.876899:0.339839:0.876899:0.000000
5:@0.339839:0.909725:0.348822:0.909725:0.348822:0.893291:0.339839:0.893291:0.000000
4:@0.496848:0.893332:0.505830:0.893332:0.505830:0.876899:0.496848:0.876899:0.000000
5:@0.496848:0.909725:0.505830:0.909725:0.505830:0.893291:0.496848:0.893291:0.000000
2:@0.417543:0.893332:0.426525:0.893332:0.426525:0.876899:0.417543:0.876899:0.000000
5:@0.417543:0.909725:0.426525:0.909725:0.426525:0.893291:0.417543:0.893291:0.000000
2:@0.598874:0.893332:0.607857:0.893332:0.607857:0.876899:0.598874:0.876899:0.000000
5:@0.598874:0.909725:0.607857:0.909725:0.607857:0.893291:0.598874:0.893291:0.000000
Competencia :@0.078581:0.143115:0.187141:0.143115:0.187141:0.126168:0.078581:0.126168:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática :@0.078581:0.159757:0.176057:0.159757:0.176057:0.142810:0.078581:0.142810:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Una curiosidad sobre :@0.082576:0.179354:0.225921:0.179354:0.225921:0.164414:0.082576:0.164414:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
las aplicaciones de :@0.082576:0.194483:0.209101:0.194483:0.209101:0.179543:0.082576:0.179543:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
logaritmos en la vida real :@0.082576:0.209611:0.250942:0.209611:0.250942:0.194672:0.082576:0.194672:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
es la de Benjamin Franklin, :@0.082576:0.224740:0.259500:0.224740:0.259500:0.209801:0.082576:0.209801:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
el famoso científico. En :@0.082576:0.239869:0.237418:0.239869:0.237418:0.224930:0.082576:0.224930:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
su testamento, Franklin :@0.082576:0.254998:0.238954:0.254998:0.238954:0.240058:0.082576:0.240058:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
donaba 1000 libras a los :@0.082576:0.270127:0.244775:0.270127:0.244775:0.255187:0.082576:0.255187:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
habitantes de Boston, :@0.082576:0.285256:0.229397:0.285256:0.229397:0.270316:0.082576:0.270316:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
con la condición de que :@0.082576:0.300385:0.245965:0.300385:0.245965:0.285445:0.082576:0.285445:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
se prestasen al 5 % a :@0.082576:0.315514:0.221261:0.315514:0.221261:0.300574:0.082576:0.300574:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
artesanos jóvenes. Según :@0.082576:0.330643:0.253039:0.330643:0.253039:0.315703:0.082576:0.315703:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Franklin, al cabo de 100 :@0.082576:0.345772:0.240513:0.345772:0.240513:0.330832:0.082576:0.330832:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
años la suma se habría :@0.082576:0.360901:0.235082:0.360901:0.235082:0.345961:0.082576:0.345961:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
convertido en 131 000 :@0.082576:0.376030:0.234735:0.376030:0.234735:0.361090:0.082576:0.361090:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
libras. Comprobemos si :@0.082576:0.391159:0.240810:0.391159:0.240810:0.376219:0.082576:0.376219:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
esto es cierto.:@0.082576:0.406288:0.172653:0.406288:0.172653:0.391348:0.082576:0.391348:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El capital final al cabo de :@0.082576:0.424985:0.247783:0.424985:0.247783:0.410045:0.082576:0.410045:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
esos 100 años será: :@0.082576:0.440113:0.211544:0.440113:0.211544:0.425174:0.082576:0.425174:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.082576:0.458810:0.089353:0.458810:0.089353:0.443896:0.082576:0.443896:0.000000
 = 1000 · 1,05 . Para :@0.089286:0.458810:0.227966:0.458823:0.227966:0.443883:0.089286:0.443870:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
100:@0.175884:0.453310:0.190088:0.453310:0.190088:0.444600:0.175884:0.444600:0.000000:0.000000:0.000000
calcular esa enorme :@0.082572:0.473952:0.218210:0.473952:0.218210:0.459012:0.082572:0.459012:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
potencia, usaremos los :@0.082572:0.489081:0.237048:0.489081:0.237048:0.474141:0.082572:0.474141:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
logaritmos::@0.082572:0.504210:0.156531:0.504210:0.156531:0.489270:0.082572:0.489270:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.082576:0.522830:0.087998:0.522830:0.087998:0.510898:0.082576:0.510898:0.000000
 = 1000 · 1,05 ; :@0.087944:0.522830:0.173807:0.522830:0.173807:0.510878:0.087944:0.510878:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
100:@0.157222:0.518420:0.168586:0.518420:0.168586:0.511452:0.157222:0.511452:0.000000:0.000000:0.000000
log x:@0.082574:0.536718:0.106912:0.536718:0.106912:0.524786:0.082574:0.524786:0.000000:0.000000:0.000000:0.000000:0.000000
   = :@0.098612:0.536718:0.120593:0.536718:0.120593:0.524766:0.098612:0.524766:0.000000:0.000000:0.000000:0.000000:0.000000
log:@0.120527:0.536718:0.136604:0.536718:0.136604:0.524786:0.120527:0.524786:0.000000:0.000000:0.000000
 1000 + 100 · :@0.136564:0.536718:0.206565:0.536718:0.206565:0.524766:0.136564:0.524766:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
log:@0.206445:0.536718:0.222523:0.536718:0.222523:0.524786:0.206445:0.524786:0.000000:0.000000:0.000000
 1,05;:@0.222483:0.536718:0.249404:0.536718:0.249404:0.524766:0.222483:0.524766:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
log x:@0.082574:0.550606:0.106912:0.550606:0.106912:0.538675:0.082574:0.538675:0.000000:0.000000:0.000000:0.000000:0.000000
   = 3 + 100 · 0,021 2 = 5,12;:@0.098612:0.550606:0.243447:0.550606:0.243447:0.538655:0.098612:0.538655:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.082574:0.567521:0.087996:0.567521:0.087996:0.555589:0.082574:0.555589:0.000000
 = 10  = 131 825,67 libras:@0.087942:0.567521:0.228538:0.567526:0.228538:0.555574:0.087942:0.555569:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5,12:@0.114564:0.563116:0.127254:0.563116:0.127254:0.556148:0.114564:0.556148:0.000000:0.000000:0.000000:0.000000
Adaptado de: :@0.082576:0.588604:0.166321:0.588604:0.166321:0.575158:0.082576:0.575158:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
https://docs.google.com/:@0.082576:0.605794:0.234403:0.605794:0.234403:0.592348:0.082576:0.592348:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
presentation/d/1Dxguar:@0.082576:0.619410:0.227361:0.619410:0.227361:0.605964:0.082576:0.605964:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u5WCw4hHwQWNPj6IN:@0.082576:0.633026:0.227735:0.633026:0.227735:0.619581:0.082576:0.619581:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
mEEkztPs38hikZeiMcO4/:@0.082576:0.646642:0.229559:0.646642:0.229559:0.633197:0.082576:0.633197:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
htmlpresent?hl=es:@0.082576:0.661768:0.194305:0.661768:0.194305:0.648322:0.082576:0.648322:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.082576:0.817390:0.092034:0.817390:0.092034:0.809100:0.082576:0.809100:0.000000
 :@0.092034:0.817934:0.094451:0.817934:0.094451:0.808077:0.092034:0.808077:0.000000
Benjamin Franklin (1706 - 1790).:@0.094451:0.817934:0.234251:0.817934:0.234251:0.808077:0.094451:0.808077:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Indaga escribe:@0.082576:0.840705:0.194470:0.840705:0.194470:0.825551:0.082576:0.825551:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 y :@0.130535:0.840705:0.145094:0.840705:0.145094:0.825765:0.130535:0.825765:0.000000:0.000000:0.000000
 otras :@0.194375:0.840705:0.234218:0.840705:0.234218:0.825765:0.194375:0.825765:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
aplicaciones de los :@0.082576:0.855834:0.210406:0.855834:0.210406:0.840894:0.082576:0.840894:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
logaritmos en la vida :@0.082576:0.870963:0.223604:0.870963:0.223604:0.856023:0.082576:0.856023:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cotidiana.:@0.082576:0.886092:0.146683:0.886092:0.146683:0.871152:0.082576:0.871152:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
MUESTRA EDITORIAL:@0.248902:0.947499:0.888171:0.113285:0.743922:0.050540:0.104653:0.884754:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 Muestra editorial solo para fines didácticos – Prohibida su venta:@0.095585:0.659700:0.095585:0.341447:0.077558:0.341447:0.077558:0.659700:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000