41:@0.942772:0.974518:0.963274:0.974518:0.963274:0.956333:0.942772:0.956333:0.000000:0.000000 Pensamiento numérico:@0.721207:0.043660:0.926911:0.043660:0.926911:0.024915:0.721207:0.024915:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5. Escribe en forma exponencial las siguientes expresiones dadas en forma logarítmica.:@0.073089:0.136836:0.756348:0.136836:0.756348:0.120167:0.073089:0.120167:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a. log 32 5:@0.104633:0.167774:0.213917:0.167774:0.213917:0.151340:0.104633:0.151340:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.158302:0.170946:0.163538:0.170946:0.163538:0.161365:0.158302:0.161365:0.000000 5:@0.187467:0.167219:0.202800:0.167219:0.202800:0.153503:0.187467:0.153503:0.000000 b. log 3125 5:@0.104633:0.202284:0.231721:0.202284:0.231721:0.185850:0.104633:0.185850:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.158302:0.205456:0.163538:0.205456:0.163538:0.195875:0.158302:0.195875:0.000000 5:@0.205270:0.201729:0.220603:0.201729:0.220603:0.188014:0.205270:0.188014:0.000000 c. log 1000 3 :@0.104633:0.236794:0.240943:0.236794:0.240943:0.220361:0.104633:0.220361:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 10:@0.158302:0.239967:0.168732:0.239967:0.168732:0.230386:0.158302:0.230386:0.000000:0.000000 5:@0.210461:0.236240:0.225794:0.236240:0.225794:0.222524:0.210461:0.222524:0.000000 d. log 256 4:@0.104633:0.271305:0.222819:0.271305:0.222819:0.254871:0.104633:0.254871:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 4:@0.158302:0.274477:0.163538:0.274477:0.163538:0.264896:0.158302:0.264896:0.000000 5:@0.196368:0.270750:0.211701:0.270750:0.211701:0.257034:0.196368:0.257034:0.000000 e. log 2 1:@0.104633:0.305816:0.205016:0.305816:0.205016:0.289383:0.104633:0.289383:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.158302:0.308989:0.163538:0.308989:0.163538:0.299408:0.158302:0.299408:0.000000 5:@0.178565:0.305262:0.193898:0.305262:0.193898:0.291546:0.178565:0.291546:0.000000 f. :@0.104633:0.340327:0.115972:0.340327:0.115972:0.323893:0.104633:0.323893:0.000000:0.000000:0.000000 log 36 2:@0.134834:0.340327:0.213917:0.340327:0.213917:0.323893:0.134834:0.323893:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 6:@0.158302:0.343499:0.163538:0.343499:0.163538:0.333918:0.158302:0.333918:0.000000 5:@0.187467:0.339772:0.202800:0.339772:0.202800:0.326056:0.187467:0.326056:0.000000 6. Expresa como un solo logaritmo las expresiones :@0.073089:0.371263:0.470157:0.371263:0.470157:0.354593:0.073089:0.354593:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a. log log :@0.104633:0.402200:0.259608:0.402200:0.259608:0.385767:0.104633:0.385767:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 3:@0.158302:0.405373:0.163538:0.405373:0.163538:0.395792:0.158302:0.395792:0.000000 a:@0.167448:0.402200:0.176707:0.402200:0.176707:0.385794:0.167448:0.385794:0.000000 1:@0.178854:0.401646:0.194187:0.401646:0.194187:0.387930:0.178854:0.387930:0.000000 3:@0.219783:0.405373:0.225020:0.405373:0.225020:0.395792:0.219783:0.395792:0.000000 b:@0.228930:0.402200:0.238189:0.402200:0.238189:0.385794:0.228930:0.385794:0.000000 5:@0.240336:0.401646:0.255669:0.401646:0.255669:0.387930:0.240336:0.387930:0.000000 __________:@0.259535:0.402200:0.350908:0.402200:0.350908:0.385767:0.259535:0.385767:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 b. log log :@0.104633:0.436711:0.266399:0.436711:0.266399:0.420277:0.104633:0.420277:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 10:@0.158302:0.439883:0.168732:0.439883:0.168732:0.430302:0.158302:0.430302:0.000000:0.000000 x:@0.172639:0.436711:0.180094:0.436711:0.180094:0.420305:0.172639:0.420305:0.000000 2:@0.182241:0.436156:0.197574:0.436156:0.197574:0.422440:0.182241:0.422440:0.000000 10:@0.223169:0.439883:0.233600:0.439883:0.233600:0.430302:0.223169:0.430302:0.000000:0.000000 y:@0.237506:0.436711:0.244980:0.436711:0.244980:0.420305:0.237506:0.420305:0.000000 5:@0.247127:0.436156:0.262460:0.436156:0.262460:0.422440:0.247127:0.422440:0.000000 __________:@0.266325:0.436711:0.357699:0.436711:0.357699:0.420277:0.266325:0.420277:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 c. log log log :@0.104633:0.471221:0.313828:0.471221:0.313828:0.454787:0.104633:0.454787:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.158302:0.474394:0.163538:0.474394:0.163538:0.464812:0.158302:0.464812:0.000000 x:@0.167448:0.471221:0.174903:0.471221:0.174903:0.454815:0.167448:0.454815:0.000000 1:@0.177050:0.470666:0.192383:0.470666:0.192383:0.456951:0.177050:0.456951:0.000000 5:@0.217980:0.474394:0.223216:0.474394:0.223216:0.464812:0.217980:0.464812:0.000000 y:@0.227126:0.471221:0.234600:0.471221:0.234600:0.454815:0.227126:0.454815:0.000000 1:@0.236747:0.470666:0.252080:0.470666:0.252080:0.456951:0.236747:0.456951:0.000000 5 :@0.277674:0.474394:0.285218:0.474394:0.285218:0.464812:0.277674:0.464812:0.000000:0.000000 z:@0.285168:0.471221:0.292402:0.471221:0.292402:0.454815:0.285168:0.454815:0.000000 5:@0.294555:0.470666:0.309889:0.470666:0.309889:0.456951:0.294555:0.456951:0.000000 __________:@0.313754:0.471221:0.405128:0.471221:0.405128:0.454787:0.313754:0.454787:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 d. log log log :@0.104633:0.505733:0.300297:0.505733:0.300297:0.489299:0.104633:0.489299:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.158302:0.508905:0.163538:0.508905:0.163538:0.499324:0.158302:0.499324:0.000000 a:@0.167448:0.505733:0.176707:0.505733:0.176707:0.489327:0.167448:0.489327:0.000000 1:@0.178854:0.505178:0.194187:0.505178:0.194187:0.491462:0.178854:0.491462:0.000000 5:@0.219783:0.508905:0.225020:0.508905:0.225020:0.499324:0.219783:0.499324:0.000000 b:@0.227193:0.505733:0.236452:0.505733:0.236452:0.489327:0.227193:0.489327:0.000000 2:@0.238606:0.505178:0.253939:0.505178:0.253939:0.491462:0.238606:0.491462:0.000000 5:@0.279533:0.508905:0.284770:0.508905:0.284770:0.499324:0.279533:0.499324:0.000000 c:@0.288682:0.505733:0.296339:0.505733:0.296339:0.489327:0.288682:0.489327:0.000000 5 :@0.298486:0.505178:0.318329:0.505178:0.318329:0.491462:0.298486:0.491462:0.000000:0.000000 __________:@0.318237:0.505733:0.409611:0.505733:0.409611:0.489299:0.318237:0.489299:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 7. Una población de bacterias comienza con 50 bacterias y se triplica cada hora que haya transcurrido. Si la cantidad de :@0.073089:0.536417:0.931208:0.536417:0.931208:0.519747:0.073089:0.519747:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 bacterias al cabo de horas está dada por la expresión 50 3 . ¿Cuántas horas habrán transcurrido para que el :@0.103214:0.552809:0.930881:0.552806:0.930881:0.536137:0.103214:0.536139:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.255277:0.552809:0.263394:0.552809:0.263394:0.536126:0.255277:0.536126:0.000000 3:@0.534920:0.552254:0.550253:0.552254:0.550253:0.538539:0.534920:0.538539:0.000000 x:@0.563495:0.546743:0.568464:0.546743:0.568464:0.537024:0.563495:0.537024:0.000000 número de bacterias sea igual a 12 150?:@0.103210:0.569196:0.385467:0.569196:0.385467:0.552527:0.103210:0.552527:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 8. El tamaño de cierto cultivo de bacterias se duplica cada 60 minutos. Supongamos que el cultivo tiene :@0.073087:0.739888:0.890008:0.739888:0.890008:0.723219:0.073087:0.723219:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 inicialmente 1000 bacterias y que, después de horas es de 1000 2 ¿cuántas horas se necesitan para :@0.103212:0.756281:0.911182:0.756278:0.911182:0.739608:0.103212:0.739611:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 n:@0.462908:0.756281:0.472738:0.756281:0.472738:0.739597:0.462908:0.739597:0.000000 3:@0.610571:0.755726:0.625905:0.755726:0.625905:0.742010:0.610571:0.742010:0.000000 n-1:@0.639549:0.750214:0.654434:0.750214:0.654434:0.740496:0.639549:0.740496:0.000000:0.000000:0.000000 que el cultivo llegue a un número de 1 024 000 bacterias? :@0.103208:0.772668:0.548469:0.772668:0.548469:0.755998:0.103208:0.755998:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 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