142:@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
8.1 Función logarítmica:@0.293660:0.241000:0.478099:0.241000:0.478099:0.224053:0.293660:0.224053:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sean   > 0 con   ≠ 1 y   la función de   en :@0.293660:0.268362:0.605277:0.268362:0.605277:0.251928:0.293660:0.251928:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.333088:0.268362:0.342347:0.268362:0.342347:0.251956:0.333088:0.251956:0.000000
a:@0.405576:0.268362:0.414835:0.268362:0.414835:0.251956:0.405576:0.251956:0.000000
f:@0.458442:0.268362:0.463136:0.268362:0.463136:0.251956:0.458442:0.251956:0.000000
ℝ:@0.565425:0.268945:0.578715:0.268945:0.578715:0.251290:0.565425:0.251290:0.000000
ℝ:@0.605203:0.268945:0.618493:0.268945:0.618493:0.251290:0.605203:0.251290:0.000000
+:@0.618423:0.261038:0.624819:0.261038:0.624819:0.251457:0.618423:0.251457:0.000000
, definida como  ( ) =      :@0.624771:0.268363:0.811297:0.268363:0.811297:0.251930:0.624771:0.251930:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.741400:0.268363:0.758279:0.268363:0.758279:0.251957:0.741400:0.251957:0.000000:0.000000:0.000000
a:@0.781841:0.268363:0.791099:0.268363:0.791099:0.251957:0.781841:0.251957:0.000000
x:@0.791029:0.262298:0.795375:0.262298:0.795375:0.252734:0.791029:0.252734:0.000000
x :@0.811224:0.268363:0.821918:0.268363:0.821918:0.251957:0.811224:0.251957:0.000000:0.000000
∈ ℝ:@0.821881:0.268946:0.854389:0.268946:0.854389:0.251292:0.821881:0.251292:0.000000:0.000000:0.000000
  . Tenemos :@0.837123:0.268363:0.931011:0.268363:0.931011:0.251930:0.837123:0.251930:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Dom f:@0.293685:0.285005:0.338581:0.285005:0.338581:0.268599:0.293685:0.268599:0.000000:0.000000:0.000000:0.000000:0.000000
( ) =  , :@0.329082:0.285005:0.382445:0.285005:0.382445:0.268571:0.329082:0.268571:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ℝ:@0.362087:0.285588:0.375377:0.285588:0.375377:0.267934:0.362087:0.267934:0.000000
Rec f:@0.382353:0.285005:0.416093:0.285005:0.416093:0.268599:0.382353:0.268599:0.000000:0.000000:0.000000:0.000000:0.000000
( ) = :@0.406595:0.285005:0.439710:0.285005:0.439710:0.268571:0.406595:0.268571:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ℝ:@0.439600:0.285588:0.452890:0.285588:0.452890:0.267934:0.439600:0.267934:0.000000
+:@0.452799:0.277679:0.459195:0.277679:0.459195:0.268098:0.452799:0.268098:0.000000
. La función es biyectiva.:@0.459148:0.285005:0.633929:0.285005:0.633929:0.268571:0.459148:0.268571:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1. Inyectiva:  ,      ,   ≠ :@0.293660:0.312367:0.507894:0.312367:0.507894:0.295698:0.293660:0.295698:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x x:@0.399512:0.312367:0.427387:0.312367:0.427387:0.295961:0.399512:0.295961:0.000000:0.000000:0.000000
1:@0.406908:0.315540:0.412414:0.315540:0.412414:0.305821:0.406908:0.305821:0.000000
2:@0.427314:0.315540:0.432819:0.315540:0.432819:0.305821:0.427314:0.305821:0.000000
∈ ℝ:@0.436601:0.312950:0.468961:0.312950:0.468961:0.295295:0.436601:0.295295:0.000000:0.000000:0.000000
x:@0.476434:0.312367:0.483889:0.312367:0.483889:0.295961:0.476434:0.295961:0.000000
1:@0.483805:0.315540:0.489311:0.315540:0.489311:0.305821:0.483805:0.305821:0.000000
x:@0.507802:0.312367:0.515257:0.312367:0.515257:0.295961:0.507802:0.295961:0.000000
2 :@0.515195:0.315540:0.522932:0.315540:0.522932:0.305821:0.515195:0.305821:0.000000:0.000000
Þ:@0.522884:0.311812:0.538217:0.311812:0.538217:0.298097:0.522884:0.298097:0.000000
 :@0.538125:0.312367:0.542028:0.312367:0.542028:0.295698:0.538125:0.295698:0.000000
a:@0.541954:0.312367:0.551213:0.312367:0.551213:0.295961:0.541954:0.295961:0.000000
x:@0.551142:0.306303:0.555489:0.306303:0.555489:0.296739:0.551142:0.296739:0.000000
1:@0.555446:0.306303:0.560951:0.306303:0.560951:0.296585:0.555446:0.296585:0.000000
 =  ( ) ≠  ( ) = :@0.560910:0.312367:0.672175:0.312367:0.672175:0.295698:0.560910:0.295698:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.579446:0.312367:0.596675:0.312367:0.596675:0.295961:0.579446:0.295961:0.000000:0.000000:0.000000
1:@0.596617:0.315540:0.602122:0.315540:0.602122:0.305821:0.596617:0.305821:0.000000
f x:@0.625767:0.312367:0.642996:0.312367:0.642996:0.295961:0.625767:0.295961:0.000000:0.000000:0.000000
2:@0.642933:0.315540:0.648438:0.315540:0.648438:0.305821:0.642933:0.305821:0.000000
a:@0.672083:0.312367:0.681342:0.312367:0.681342:0.295961:0.672083:0.295961:0.000000
x:@0.681277:0.306303:0.685623:0.306303:0.685623:0.296739:0.681277:0.296739:0.000000
2:@0.685580:0.306303:0.691085:0.306303:0.691085:0.296585:0.685580:0.296585:0.000000
.:@0.691044:0.312367:0.694855:0.312367:0.694855:0.295698:0.691044:0.295698:0.000000
2. Sobreyectiva: :@0.293660:0.336157:0.429657:0.336157:0.429657:0.319488:0.293660:0.319488:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Rec f:@0.429553:0.336157:0.463643:0.336157:0.463643:0.319751:0.429553:0.319751:0.000000:0.000000:0.000000:0.000000:0.000000
( ) = :@0.453795:0.336157:0.487351:0.336157:0.487351:0.319488:0.453795:0.319488:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ℝ:@0.487259:0.336740:0.500549:0.336740:0.500549:0.319086:0.487259:0.319086:0.000000
+:@0.500459:0.328833:0.506855:0.328833:0.506855:0.319114:0.500459:0.319114:0.000000
 :@0.506809:0.336157:0.510712:0.336157:0.510712:0.319488:0.506809:0.319488:0.000000
⇔:@0.510638:0.335741:0.529818:0.335741:0.529818:0.318753:0.510638:0.318753:0.000000
 :@0.529726:0.336157:0.533629:0.336157:0.533629:0.319488:0.529726:0.319488:0.000000
∀ ∈ ℝ ∃ ∈ ℝ:@0.533555:0.336740:0.658328:0.336740:0.658328:0.319086:0.533555:0.319086:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.545741:0.336157:0.553214:0.336157:0.553214:0.319751:0.545741:0.319751:0.000000
   :@0.553140:0.336157:0.576113:0.336157:0.576113:0.319488:0.553140:0.319488:0.000000:0.000000:0.000000
+:@0.589227:0.328833:0.595623:0.328833:0.595623:0.319114:0.589227:0.319114:0.000000
, :@0.595578:0.336157:0.603217:0.336157:0.603217:0.319488:0.595578:0.319488:0.000000:0.000000
x :@0.615329:0.336157:0.626023:0.336157:0.626023:0.319751:0.615329:0.319751:0.000000:0.000000
  , tal que   =  ( ) =  .:@0.641209:0.336157:0.806108:0.336157:0.806108:0.319488:0.641209:0.319488:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.722017:0.336157:0.729490:0.336157:0.729490:0.319751:0.722017:0.319751:0.000000
f x:@0.747953:0.336157:0.765182:0.336157:0.765182:0.319751:0.747953:0.319751:0.000000:0.000000:0.000000
a:@0.788799:0.336157:0.798057:0.336157:0.798057:0.319751:0.788799:0.319751:0.000000
x:@0.797990:0.330094:0.802337:0.330094:0.802337:0.320529:0.797990:0.320529:0.000000
La función inversa de la función   se define a continuación::@0.293668:0.367097:0.716428:0.367097:0.716428:0.350664:0.293668:0.350664:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.526649:0.367097:0.531343:0.367097:0.531343:0.350691:0.526649:0.350691:0.000000
f:@0.538098:0.397011:0.542792:0.397011:0.542792:0.380605:0.538098:0.380605:0.000000
–1:@0.542735:0.390940:0.553295:0.390940:0.553295:0.381359:0.542735:0.381359:0.000000:0.000000
: :@0.553244:0.397004:0.560405:0.397004:0.560405:0.380570:0.553244:0.380570:0.000000:0.000000
ℝ:@0.572572:0.387629:0.585862:0.387629:0.585862:0.369974:0.572572:0.369974:0.000000
+:@0.585854:0.379722:0.592249:0.379722:0.592249:0.370141:0.585854:0.370141:0.000000
   :@0.592249:0.387046:0.616712:0.387046:0.616712:0.370612:0.592249:0.370612:0.000000:0.000000:0.000000
:@0.596280:0.386505:0.612681:0.386505:0.612681:0.370709:0.596280:0.370709:0.000000
ℝ:@0.616712:0.387629:0.630002:0.387629:0.630002:0.369974:0.616712:0.369974:0.000000
y:@0.572572:0.407266:0.580045:0.407266:0.580045:0.390860:0.572572:0.390860:0.000000
   :@0.580045:0.407266:0.604508:0.407266:0.604508:0.390832:0.580045:0.390832:0.000000:0.000000:0.000000
:@0.584076:0.406725:0.600477:0.406725:0.600477:0.390929:0.584076:0.390929:0.000000
f  y:@0.604508:0.407266:0.635463:0.407262:0.635463:0.390856:0.604508:0.390860:0.000000:0.000000:0.000000:0.000000
–1:@0.612509:0.401198:0.623111:0.401198:0.623111:0.391617:0.612509:0.391617:0.000000:0.000000
( ) = :@0.623111:0.407262:0.659374:0.407262:0.659374:0.390828:0.623111:0.390828:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x.:@0.659374:0.407262:0.670160:0.407262:0.670160:0.390856:0.659374:0.390856:0.000000:0.000000
Esta función está relacionada con la función directa   mediante la siguiente equivalencia::@0.293660:0.431514:0.926892:0.431514:0.926892:0.415080:0.293660:0.415080:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.664973:0.431514:0.669667:0.431514:0.669667:0.415108:0.664973:0.415108:0.000000
y:@0.465825:0.455298:0.473298:0.455298:0.473298:0.438892:0.465825:0.438892:0.000000
 =  ( ) =   :@0.473225:0.455298:0.549959:0.455304:0.549959:0.438870:0.473225:0.438864:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.492018:0.455298:0.508898:0.455298:0.508898:0.438892:0.492018:0.438892:0.000000:0.000000:0.000000
a:@0.532404:0.455298:0.541663:0.455298:0.541663:0.438892:0.532404:0.438892:0.000000
x:@0.541621:0.449240:0.545967:0.449240:0.545967:0.439676:0.541621:0.439676:0.000000
⇔:@0.549886:0.454888:0.569066:0.454888:0.569066:0.437900:0.549886:0.437900:0.000000
   =  ( ),         ,     :@0.568974:0.455304:0.732077:0.455304:0.732077:0.438870:0.568974:0.438870:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.572932:0.455304:0.580387:0.455304:0.580387:0.438898:0.572932:0.438898:0.000000
f y:@0.599107:0.455304:0.626990:0.455304:0.626990:0.438898:0.599107:0.438898:0.000000:0.000000:0.000000
–1:@0.604204:0.449240:0.614764:0.449240:0.614764:0.439659:0.604204:0.439659:0.000000:0.000000
x:@0.650644:0.455304:0.658099:0.455304:0.658099:0.438898:0.650644:0.438898:0.000000
∈ ℝ ∈ ℝ:@0.661983:0.455887:0.745294:0.455887:0.745294:0.438232:0.661983:0.438232:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.701448:0.455304:0.708921:0.455304:0.708921:0.438898:0.701448:0.438898:0.000000
+:@0.745188:0.447980:0.751584:0.447980:0.751584:0.438399:0.745188:0.438399:0.000000
.:@0.751537:0.455304:0.754740:0.455304:0.754740:0.438870:0.751537:0.438870:0.000000
Al número real :@0.293657:0.482666:0.404446:0.482666:0.404446:0.466232:0.293657:0.466232:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f  y:@0.404284:0.482666:0.435431:0.482667:0.435431:0.466261:0.404284:0.466260:0.000000:0.000000:0.000000:0.000000
–1:@0.412645:0.476603:0.423204:0.476603:0.423204:0.467023:0.412645:0.467023:0.000000:0.000000
( ) se lo denomina logaritmo de base   de   y se lo nota :@0.423153:0.482667:0.829862:0.482667:0.829862:0.466234:0.423153:0.466234:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.696133:0.482667:0.705392:0.482667:0.705392:0.466261:0.696133:0.466261:0.000000
x:@0.731990:0.482667:0.739445:0.482667:0.739445:0.466261:0.731990:0.466261:0.000000
log y:@0.829696:0.482667:0.869411:0.482667:0.869411:0.466261:0.829696:0.466261:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.851775:0.485840:0.857173:0.485840:0.857173:0.476275:0.851775:0.476275:0.000000
( ). Así,:@0.857133:0.482667:0.905537:0.482667:0.905537:0.466234:0.857133:0.466234:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.540050:0.502887:0.547523:0.502887:0.547523:0.486481:0.540050:0.486481:0.000000
 =   :@0.547449:0.502887:0.583770:0.502882:0.583770:0.486448:0.547449:0.486453:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.566243:0.502887:0.575502:0.502887:0.575502:0.486481:0.566243:0.486481:0.000000
x:@0.575432:0.496818:0.579778:0.496818:0.579778:0.487254:0.575432:0.487254:0.000000
⇔:@0.583697:0.502466:0.602877:0.502466:0.602877:0.485478:0.583697:0.485478:0.000000
   = :@0.602785:0.502882:0.633010:0.502882:0.633010:0.486448:0.602785:0.486448:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.606742:0.502882:0.614197:0.502882:0.614197:0.486476:0.606742:0.486476:0.000000
log y:@0.632918:0.502882:0.672602:0.502882:0.672602:0.486476:0.632918:0.486476:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.654964:0.506055:0.660362:0.506055:0.660362:0.496490:0.654964:0.496490:0.000000
( ).:@0.660324:0.502882:0.680535:0.502882:0.680535:0.486448:0.660324:0.486448:0.000000:0.000000:0.000000:0.000000
Como se ha dicho, la función exponencial dada como :@0.293652:0.530244:0.681710:0.530244:0.681710:0.513810:0.293652:0.513810:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Exp x:@0.681124:0.530244:0.723180:0.530245:0.723180:0.513839:0.681124:0.513838:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.705641:0.533418:0.711039:0.533418:0.711039:0.523853:0.705641:0.523853:0.000000
( ) =  ,       es biyectiva, por :@0.710976:0.530245:0.930958:0.530245:0.930958:0.513812:0.710976:0.513812:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a x:@0.745655:0.530245:0.773117:0.530245:0.773117:0.513839:0.745655:0.513839:0.000000:0.000000:0.000000
x:@0.754807:0.524181:0.759153:0.524181:0.759153:0.514617:0.754807:0.514617:0.000000
∈ ℝ:@0.776504:0.530828:0.808478:0.530828:0.808478:0.513174:0.776504:0.513174:0.000000:0.000000:0.000000
lo tanto, existe la función inversa notada como :@0.293663:0.546887:0.634991:0.546887:0.634991:0.530453:0.293663:0.530453:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Log:@0.634603:0.546887:0.659920:0.546887:0.659920:0.530481:0.634603:0.530481:0.000000:0.000000:0.000000
a:@0.659866:0.550060:0.665264:0.550060:0.665264:0.540495:0.659866:0.540495:0.000000
, esto es,:@0.665226:0.546887:0.725771:0.546887:0.725771:0.530453:0.665226:0.530453:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Log:@0.538068:0.577023:0.563386:0.577023:0.563386:0.560617:0.538068:0.560617:0.000000:0.000000:0.000000
a:@0.563333:0.580194:0.568731:0.580194:0.568731:0.570629:0.563333:0.570629:0.000000
: :@0.568693:0.577022:0.575853:0.577022:0.575853:0.560588:0.568693:0.560588:0.000000:0.000000
ℝ:@0.588021:0.571003:0.601311:0.571003:0.601311:0.553349:0.588021:0.553349:0.000000
+:@0.601302:0.563088:0.607698:0.563088:0.607698:0.553507:0.601302:0.553507:0.000000
   :@0.607698:0.570413:0.632161:0.570413:0.632161:0.553979:0.607698:0.553979:0.000000:0.000000:0.000000
:@0.611729:0.569872:0.628130:0.569872:0.628130:0.554076:0.611729:0.554076:0.000000
ℝ:@0.632161:0.570995:0.645451:0.570995:0.645451:0.553341:0.632161:0.553341:0.000000
y:@0.588021:0.589121:0.595494:0.589121:0.595494:0.572715:0.588021:0.572715:0.000000
   :@0.595494:0.589121:0.619957:0.589121:0.619957:0.572687:0.595494:0.572687:0.000000:0.000000:0.000000
:@0.599525:0.588580:0.615926:0.588580:0.615926:0.572784:0.599525:0.572784:0.000000
log y:@0.619957:0.589121:0.659954:0.589116:0.659954:0.572710:0.619957:0.572715:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.642205:0.592288:0.647603:0.592288:0.647603:0.582724:0.642205:0.582724:0.000000
( ),:@0.647603:0.589116:0.668035:0.589116:0.668035:0.572682:0.647603:0.572682:0.000000:0.000000:0.000000:0.000000
donde :@0.293660:0.611532:0.345937:0.611532:0.345937:0.595098:0.293660:0.595098:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
log y:@0.345820:0.611532:0.385512:0.611532:0.385512:0.595126:0.345820:0.595126:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.367876:0.614704:0.373274:0.614704:0.373274:0.605140:0.367876:0.605140:0.000000
( ) es la imagen de la función :@0.373235:0.611532:0.587992:0.611532:0.587992:0.595098:0.373235:0.595098:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Log:@0.587716:0.611532:0.613033:0.611532:0.613033:0.595126:0.587716:0.595126:0.000000:0.000000:0.000000
a:@0.612971:0.614704:0.618369:0.614704:0.618369:0.605140:0.612971:0.605140:0.000000
 en  .:@0.618329:0.611532:0.655456:0.611532:0.655456:0.595098:0.618329:0.595098:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.644854:0.611532:0.652327:0.611532:0.652327:0.595126:0.644854:0.595126:0.000000
La función :@0.293643:0.638894:0.373172:0.638894:0.373172:0.622460:0.293643:0.622460:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Log:@0.372739:0.638894:0.398053:0.638894:0.398053:0.622488:0.372739:0.622488:0.000000:0.000000:0.000000
a:@0.398007:0.642067:0.403405:0.642067:0.403405:0.632503:0.398007:0.632503:0.000000
 se llama función logaritmo de base   y el número real :@0.403364:0.638895:0.794752:0.638895:0.794752:0.622461:0.403364:0.622461:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.662538:0.638895:0.671797:0.638895:0.671797:0.622489:0.662538:0.622489:0.000000
log x:@0.794334:0.638895:0.833977:0.638895:0.833977:0.622489:0.794334:0.622489:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.816379:0.642067:0.821777:0.642067:0.821777:0.632503:0.816379:0.632503:0.000000
( ) con   > 0 se :@0.821736:0.638895:0.930898:0.638895:0.930898:0.622461:0.821736:0.622461:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.873377:0.638895:0.880832:0.638895:0.880832:0.622489:0.873377:0.622489:0.000000
llama logaritmo de base   de  .:@0.293632:0.655537:0.519139:0.655537:0.519139:0.639103:0.293632:0.639103:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.472697:0.655537:0.481956:0.655537:0.481956:0.639131:0.472697:0.639131:0.000000
x:@0.508555:0.655537:0.516010:0.655537:0.516010:0.639131:0.508555:0.639131:0.000000
El :@0.293613:0.682899:0.310920:0.682899:0.310920:0.666465:0.293613:0.666465:0.000000:0.000000:0.000000
Dom Log:@0.313898:0.682899:0.382007:0.682899:0.382007:0.666493:0.313898:0.666493:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.350549:0.682899:0.355427:0.682899:0.355427:0.666465:0.350549:0.666465:0.000000
a:@0.382407:0.686072:0.387804:0.686072:0.387804:0.676508:0.382407:0.676508:0.000000
) = :@0.388009:0.682900:0.415730:0.682900:0.415730:0.666466:0.388009:0.666466:0.000000:0.000000:0.000000:0.000000
ℝ:@0.418712:0.683483:0.432002:0.683483:0.432002:0.665828:0.418712:0.665828:0.000000
+:@0.432486:0.675576:0.438882:0.675576:0.438882:0.665995:0.432486:0.665995:0.000000
, :@0.439131:0.682900:0.446788:0.682900:0.446788:0.666466:0.439131:0.666466:0.000000:0.000000
Rec Log:@0.449752:0.682900:0.506706:0.682900:0.506706:0.666494:0.449752:0.666494:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.475248:0.682900:0.480126:0.682900:0.480126:0.666466:0.475248:0.666466:0.000000
a:@0.507074:0.686072:0.512472:0.686072:0.512472:0.676508:0.507074:0.676508:0.000000
) =  , la función exponencial y la logarítmica están :@0.512676:0.682900:0.930764:0.682900:0.930764:0.666466:0.512676:0.666466:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ℝ:@0.543380:0.683483:0.556670:0.683483:0.556670:0.665828:0.543380:0.665828:0.000000
relacionadas mediante la siguiente equivalencia::@0.293648:0.699542:0.644027:0.699542:0.644027:0.683108:0.293648:0.683108:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.453663:0.719762:0.461136:0.719762:0.461136:0.703356:0.453663:0.703356:0.000000
 = :@0.461062:0.719762:0.479948:0.719762:0.479948:0.703328:0.461062:0.703328:0.000000:0.000000:0.000000
exp x:@0.479856:0.719762:0.521800:0.719757:0.521800:0.703351:0.479856:0.703356:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.504181:0.722929:0.509578:0.722929:0.509578:0.713364:0.504181:0.713364:0.000000
( ) :@0.509540:0.719757:0.530561:0.719757:0.530561:0.703323:0.509540:0.703323:0.000000:0.000000:0.000000:0.000000
⇔:@0.530469:0.719341:0.549650:0.719341:0.549650:0.702352:0.530469:0.702352:0.000000
   = :@0.549558:0.719757:0.579782:0.719757:0.579782:0.703323:0.549558:0.703323:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.553515:0.719757:0.560970:0.719757:0.560970:0.703351:0.553515:0.703351:0.000000
log y:@0.579690:0.719757:0.619385:0.719757:0.619385:0.703351:0.579690:0.703351:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.601749:0.722929:0.607147:0.722929:0.607147:0.713364:0.601749:0.713364:0.000000
( ),          ,         :@0.607107:0.719757:0.744223:0.719757:0.744223:0.703323:0.607107:0.703323:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.646977:0.719757:0.654432:0.719757:0.654432:0.703351:0.646977:0.703351:0.000000
∈ ℝ:@0.658316:0.720339:0.690805:0.720339:0.690805:0.702685:0.658316:0.702685:0.000000:0.000000:0.000000
y:@0.713593:0.719757:0.721067:0.719757:0.721067:0.703351:0.713593:0.703351:0.000000
∈ ℝ:@0.724950:0.720339:0.757439:0.720339:0.757439:0.702685:0.724950:0.702685:0.000000:0.000000:0.000000
+:@0.757335:0.712432:0.763731:0.712432:0.763731:0.702851:0.757335:0.702851:0.000000
.:@0.763684:0.719757:0.766887:0.719757:0.766887:0.703323:0.763684:0.703323:0.000000
Nota que cuando la base   =  ,   > 0 se escribe  ( ), lo que se denomina logaritmo natural :@0.293655:0.747119:0.931043:0.747119:0.931043:0.730685:0.293655:0.730685:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a e y:@0.473126:0.747119:0.521150:0.747119:0.521150:0.730713:0.473126:0.730713:0.000000:0.000000:0.000000:0.000000:0.000000
ln y:@0.623660:0.747119:0.648657:0.747119:0.648657:0.730713:0.623660:0.730713:0.000000:0.000000:0.000000:0.000000
de  , o también, logaritmo neperiano. Tenemos::@0.293655:0.763761:0.634302:0.763761:0.634302:0.747327:0.293655:0.747327:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.316112:0.763761:0.323585:0.763761:0.323585:0.747355:0.316112:0.747355:0.000000
y:@0.533262:0.783980:0.540736:0.783980:0.540736:0.767574:0.533262:0.767574:0.000000
 = :@0.540662:0.783980:0.559548:0.783980:0.559548:0.767547:0.540662:0.767547:0.000000:0.000000:0.000000
exp x:@0.559456:0.783980:0.596013:0.783980:0.596013:0.767574:0.559456:0.767574:0.000000:0.000000:0.000000:0.000000:0.000000
( ) :@0.583753:0.783980:0.604775:0.783980:0.604775:0.767547:0.583753:0.767547:0.000000:0.000000:0.000000:0.000000
⇔:@0.604682:0.783564:0.623863:0.783564:0.623863:0.766576:0.604682:0.766576:0.000000
   =  ( ).:@0.623771:0.783980:0.687276:0.783980:0.687276:0.767547:0.623771:0.767547:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.627728:0.783980:0.635183:0.783980:0.635183:0.767574:0.627728:0.767574:0.000000
ln y:@0.653903:0.783980:0.679342:0.783980:0.679342:0.767574:0.653903:0.767574:0.000000:0.000000:0.000000:0.000000
Cuando   = 10,   > 0, se escribe :@0.293637:0.811342:0.525929:0.811342:0.525929:0.794909:0.293637:0.794909:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.355264:0.811342:0.364523:0.811342:0.364523:0.794936:0.355264:0.794936:0.000000
y:@0.408111:0.811342:0.415585:0.811342:0.415585:0.794936:0.408111:0.794936:0.000000
log y:@0.525734:0.811342:0.560063:0.811342:0.560063:0.794936:0.525734:0.794936:0.000000:0.000000:0.000000:0.000000:0.000000
( ) al logaritmo de base 10 de  .  :@0.547786:0.811342:0.783859:0.811342:0.783859:0.794909:0.547786:0.794909:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.765194:0.811342:0.772667:0.811342:0.772667:0.794936:0.765194:0.794936:0.000000
Ejercicio 1:@0.293600:0.838704:0.370003:0.838704:0.370003:0.822035:0.293600:0.822035:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1. La función :@0.293660:0.866877:0.407097:0.866877:0.407097:0.850207:0.293660:0.850207:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Exp:@0.406968:0.866877:0.431653:0.866877:0.431653:0.850471:0.406968:0.850471:0.000000:0.000000:0.000000
2:@0.431607:0.870049:0.437113:0.870049:0.437113:0.860331:0.431607:0.860331:0.000000
::@0.437068:0.866877:0.440878:0.866877:0.440878:0.850207:0.437068:0.850207:0.000000
ℝ:@0.460703:0.863368:0.473993:0.863368:0.473993:0.845714:0.460703:0.845714:0.000000
   :@0.473993:0.862786:0.498456:0.862786:0.498456:0.846352:0.473993:0.846352:0.000000:0.000000:0.000000
:@0.478024:0.862245:0.494425:0.862245:0.494425:0.846449:0.478024:0.846449:0.000000
ℝ:@0.498456:0.863368:0.511746:0.863368:0.511746:0.845714:0.498456:0.845714:0.000000
+:@0.511739:0.855466:0.518135:0.855466:0.518135:0.845885:0.511739:0.845885:0.000000
x:@0.460696:0.877920:0.468151:0.877920:0.468151:0.861514:0.460696:0.861514:0.000000
   :@0.468151:0.877920:0.492614:0.877920:0.492614:0.861486:0.468151:0.861486:0.000000:0.000000:0.000000
:@0.472182:0.877379:0.488583:0.877379:0.488583:0.861583:0.472182:0.861583:0.000000
exp x:@0.492614:0.877920:0.534685:0.877920:0.534685:0.861514:0.492614:0.861514:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.517116:0.881092:0.522353:0.881092:0.522353:0.871511:0.517116:0.871511:0.000000
( ) = 2:@0.522352:0.877920:0.567578:0.877920:0.567578:0.861486:0.522352:0.861486:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.567578:0.871856:0.571925:0.871856:0.571925:0.862291:0.567578:0.862291:0.000000
 :@0.583559:0.866877:0.587462:0.866877:0.587462:0.850207:0.583559:0.850207:0.000000
es:@0.587383:0.867035:0.604568:0.867035:0.604568:0.849607:0.587383:0.849607:0.000000:0.000000
 :@0.604491:0.867035:0.608571:0.867035:0.608571:0.849607:0.604491:0.849607:0.000000
biyectiva:@0.608494:0.867035:0.680031:0.867035:0.680031:0.849607:0.608494:0.849607:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. :@0.679927:0.867035:0.687990:0.867035:0.687990:0.849607:0.679927:0.849607:0.000000:0.000000
Su función inversa está definida como :@0.323781:0.902554:0.603430:0.902554:0.603430:0.886121:0.323781:0.886121:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Log:@0.603093:0.902554:0.628410:0.902554:0.628410:0.886148:0.603093:0.886148:0.000000:0.000000:0.000000
2:@0.628358:0.905727:0.633594:0.905727:0.633594:0.896146:0.628358:0.896146:0.000000
:  :@0.633547:0.902554:0.644665:0.902554:0.644665:0.886121:0.633547:0.886121:0.000000:0.000000:0.000000
ℝ:@0.655819:0.898699:0.669110:0.898699:0.669110:0.881045:0.655819:0.881045:0.000000
+:@0.669118:0.890786:0.675514:0.890786:0.675514:0.881205:0.669118:0.881205:0.000000
   :@0.675514:0.898111:0.699977:0.898111:0.699977:0.881677:0.675514:0.881677:0.000000:0.000000:0.000000
:@0.679545:0.897570:0.695946:0.897570:0.695946:0.881774:0.679545:0.881774:0.000000
ℝ:@0.699977:0.898693:0.713267:0.898693:0.713267:0.881039:0.699977:0.881039:0.000000
x:@0.655836:0.913241:0.663291:0.913241:0.663291:0.896835:0.655836:0.896835:0.000000
   :@0.663291:0.913241:0.687754:0.913241:0.687754:0.896807:0.663291:0.896807:0.000000:0.000000:0.000000
:@0.667322:0.912700:0.683723:0.912700:0.683723:0.896904:0.667322:0.896904:0.000000
log x:@0.687754:0.913241:0.727571:0.913240:0.727571:0.896833:0.687754:0.896835:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.710002:0.916412:0.715239:0.916412:0.715239:0.906831:0.710002:0.906831:0.000000
( ):@0.715238:0.913240:0.732449:0.913240:0.732449:0.896806:0.715238:0.896806:0.000000:0.000000:0.000000
El número real :@0.323781:0.937065:0.432327:0.937065:0.432327:0.920631:0.323781:0.920631:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
log x:@0.432168:0.937065:0.471672:0.937065:0.471672:0.920659:0.432168:0.920659:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.454223:0.940237:0.459460:0.940237:0.459460:0.930656:0.454223:0.930656:0.000000
( ) se llama logaritmo de base 2 de   con   > 0. :@0.459412:0.937065:0.799818:0.937065:0.799818:0.920631:0.459412:0.920631:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.714574:0.937065:0.722029:0.937065:0.722029:0.920659:0.714574:0.920659:0.000000
x:@0.757481:0.937065:0.764936:0.937065:0.764936:0.920659:0.757481:0.920659:0.000000
Tema 8. Función logarítmica:@0.073089:0.098522:0.490291:0.098522:0.490291:0.067281:0.073089:0.067281:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Reto matemático:@0.302768:0.139665:0.425244:0.139665:0.425244:0.124259:0.302768:0.124259:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Cómo determinas si una función tiene inversa?:@0.309882:0.171944:0.643705:0.171944:0.643705:0.156257:0.309882:0.156257:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Competencia :@0.078581:0.254426:0.187141:0.254426:0.187141:0.237479:0.078581:0.237479:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática :@0.078581:0.271068:0.176057:0.271068:0.176057:0.254121:0.078581:0.254121:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A B:@0.082576:0.291926:0.110209:0.291926:0.110209:0.275519:0.082576:0.275519:0.000000:0.000000:0.000000
,   son dos conjuntos :@0.092594:0.291926:0.259800:0.291926:0.259800:0.275492:0.092594:0.275492:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(no vacíos) cualesquiera :@0.082580:0.308567:0.259897:0.308567:0.259897:0.292134:0.082580:0.292134:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y   es una función de   :@0.082580:0.325209:0.259732:0.325209:0.259732:0.308775:0.082580:0.308775:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.095778:0.325209:0.100472:0.325209:0.100472:0.308803:0.095778:0.308803:0.000000
A:@0.245816:0.325209:0.255700:0.325209:0.255700:0.308803:0.245816:0.308803:0.000000
en   que suponemos :@0.082562:0.341851:0.259732:0.341851:0.259732:0.325417:0.082562:0.325417:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
B:@0.109915:0.341851:0.118750:0.341851:0.118750:0.325445:0.109915:0.325445:0.000000
biyectiva, esto es,:@0.082562:0.358493:0.207961:0.358493:0.207961:0.342059:0.082562:0.342059:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.082562:0.394744:0.087256:0.394744:0.087256:0.378338:0.082562:0.378338:0.000000
: :@0.087182:0.394744:0.094342:0.394744:0.094342:0.378310:0.087182:0.378310:0.000000:0.000000
A:@0.105373:0.383554:0.114808:0.383554:0.114808:0.367894:0.105373:0.367894:0.000000
   :@0.114808:0.383554:0.138158:0.383554:0.138158:0.367868:0.114808:0.367868:0.000000:0.000000:0.000000
:@0.118656:0.383038:0.134311:0.383038:0.134311:0.367960:0.118656:0.367960:0.000000
B:@0.138158:0.383554:0.146592:0.383554:0.146592:0.367894:0.138158:0.367894:0.000000
x:@0.105373:0.402695:0.112489:0.402695:0.112489:0.387035:0.105373:0.387035:0.000000
    ( ),:@0.112489:0.402695:0.159804:0.402695:0.159804:0.387009:0.112489:0.387009:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.116337:0.402179:0.131991:0.402179:0.131991:0.387101:0.116337:0.387101:0.000000
f x:@0.135839:0.402695:0.152091:0.402695:0.152091:0.387035:0.135839:0.387035:0.000000:0.000000:0.000000
de modo que se :@0.082576:0.432828:0.205831:0.432828:0.205831:0.416394:0.082576:0.416394:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
verifican las dos :@0.082576:0.449469:0.200901:0.449469:0.200901:0.433036:0.082576:0.433036:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
condiciones.:@0.082576:0.466111:0.173999:0.466111:0.173999:0.449677:0.082576:0.449677:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Inyectividad: :@0.082576:0.489895:0.183339:0.489895:0.183339:0.473226:0.082576:0.473226:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x x:@0.082576:0.506537:0.110209:0.506542:0.110209:0.490136:0.082576:0.490131:0.000000:0.000000:0.000000
1:@0.089995:0.509715:0.095232:0.509715:0.095232:0.500134:0.089995:0.500134:0.000000
,      ,   ≠ :@0.095207:0.506542:0.186768:0.506542:0.186768:0.490108:0.095207:0.490108:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.110178:0.509715:0.115414:0.509715:0.115414:0.500134:0.110178:0.500134:0.000000
∈:@0.119781:0.506572:0.133023:0.506572:0.133023:0.491326:0.119781:0.491326:0.000000
A x:@0.137380:0.506542:0.162230:0.506542:0.162230:0.490136:0.137380:0.490136:0.000000:0.000000:0.000000
1:@0.162192:0.509715:0.167429:0.509715:0.167429:0.500134:0.162192:0.500134:0.000000
x:@0.187117:0.506542:0.194572:0.506542:0.194572:0.490136:0.187117:0.490136:0.000000
2  :@0.194534:0.509715:0.206287:0.509715:0.206287:0.500134:0.194534:0.500134:0.000000:0.000000:0.000000
 :@0.199745:0.506384:0.203592:0.506384:0.203592:0.490698:0.199745:0.490698:0.000000
⇒:@0.206497:0.505571:0.221361:0.505571:0.221361:0.491672:0.206497:0.491672:0.000000
   ( ) :@0.221318:0.506384:0.259560:0.506384:0.259560:0.490698:0.221318:0.490698:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.229699:0.506384:0.245880:0.506384:0.245880:0.490725:0.229699:0.490725:0.000000:0.000000:0.000000
1:@0.245845:0.509715:0.251082:0.509715:0.251082:0.500134:0.245845:0.500134:0.000000
≠  ( ). :@0.082580:0.523023:0.129470:0.523026:0.129470:0.507340:0.082580:0.507337:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.096741:0.523023:0.112852:0.523023:0.112852:0.507364:0.096741:0.507364:0.000000:0.000000:0.000000
2:@0.112789:0.526356:0.118026:0.526356:0.118026:0.516775:0.112789:0.516775:0.000000
Sobreyectividad::@0.082576:0.546973:0.209475:0.546973:0.209475:0.530303:0.082576:0.530303:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Rec f:@0.082576:0.563615:0.116316:0.563615:0.116316:0.547209:0.082576:0.547209:0.000000:0.000000:0.000000:0.000000:0.000000
( ) =  .:@0.106818:0.563615:0.151787:0.563615:0.151787:0.547181:0.106818:0.547181:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
B:@0.139822:0.563615:0.148658:0.563615:0.148658:0.547209:0.139822:0.547209:0.000000
Biyección.:@0.084437:0.625315:0.153634:0.623949:0.153107:0.608800:0.083911:0.610166:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 Aplicación :@0.153533:0.623952:0.230132:0.622440:0.229612:0.607506:0.153014:0.609017:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
biyectiva.:@0.084955:0.640439:0.146804:0.639219:0.146285:0.624284:0.084436:0.625504:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Biyectiva.:@0.085729:0.662709:0.150855:0.661424:0.150328:0.646275:0.085202:0.647560:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 Dicho de :@0.150768:0.661426:0.218082:0.660097:0.217563:0.645163:0.150249:0.646491:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
una aplicación de :@0.086255:0.677833:0.206580:0.675459:0.206061:0.660524:0.085735:0.662898:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
un conjunto en otro :@0.086780:0.692956:0.223587:0.690257:0.223067:0.675322:0.086261:0.678022:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
que cumple que su :@0.087306:0.708080:0.219074:0.705480:0.218555:0.690545:0.086787:0.693145:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
correspondencia :@0.087832:0.723204:0.202893:0.720934:0.202374:0.705999:0.087313:0.708269:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
inversa es también una :@0.088357:0.738328:0.244286:0.735251:0.243767:0.720316:0.087838:0.723393:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
aplicación.:@0.088883:0.753452:0.158874:0.752071:0.158355:0.737136:0.088364:0.738517:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Glosario:@0.137491:0.602221:0.197111:0.602221:0.197111:0.586815:0.137491:0.586815:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Función :@0.081427:0.803537:0.148483:0.803537:0.148483:0.786590:0.081427:0.786590:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
logarítmica :@0.081427:0.814881:0.175175:0.814881:0.175175:0.797934:0.081427:0.797934:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
EC. Reconoce una función logarítmica, construye su gráfica en el plano cartesiano, :@0.480907:0.965292:0.915893:0.965292:0.915893:0.953340:0.480907:0.953340:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
describe sus principales características e identifica sus componentes principales.:@0.480907:0.977395:0.902785:0.977395:0.902785:0.965444:0.480907:0.965444:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
MUESTRA EDITORIAL:@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