Respostas

2014-08-21T01:39:33-03:00
Oi Maysa ;D

use as seguintes propriedades de log:

logb^k=k\cdot logb\\\\
log_kk=1\\\\log_{\tfrac{1}{b}}=-log_b

__________________

log_{ \tfrac{1}{3}}243=-log_33^5\\\\
log_{ \tfrac{1}{3}}243=5\cdot(-log_33)\\\\
log_{ \tfrac{1}{3}}243=5\cdot(-1)\\\\
\Large\boxed{\boxed{\boxed{log_{ \tfrac{1}{3}}243=-5}}}

...........................

log_{ \tfrac{5}{3}} \dfrac{27}{125}=log_{ \tfrac{5}{3}} \dfrac{27}{125}\\\\
log_{ \tfrac{5}{3}} \dfrac{27}{125}=log_{ \tfrac{5}{3}}\dfrac{3^3}{5^3}\\\\
log_{ \tfrac{5}{3}} \dfrac{27}{125}=log_{ \tfrac{5}{3}}\left( \dfrac{3}{5}\right)^3\\\\
log_{ \tfrac{5}{3}} \dfrac{27}{125}=log_{ \tfrac{5}{3}}\left( \dfrac{5}{3}\right)^{-3}\\\\
log_{ \tfrac{5}{3}} \dfrac{27}{125}=(-3)\cdot log_{ \tfrac{5}{3}} \dfrac{5}{3}\\\\
log_{ \tfrac{5}{3}} \dfrac{27}{125}=(-3)\cdot1

\Large\boxed{\boxed{\boxed{log_{ \tfrac{5}{3}} \dfrac{27}{125}=-3}}}.\\.

............................

log_{ \tfrac{2}{3}} \dfrac{729}{64}= log_{ \tfrac{2}{3} }\dfrac{3^6}{2^6}\\\\
log_{ \tfrac{2}{3} } \dfrac{729}{64}=log_{ \tfrac{2}{3} } \dfrac{2}{3}^{-6}\\\\
log_{ \tfrac{2}{3}} \dfrac{729}{64} =(-6)\cdot log_{ \tfrac{2}{3} } \dfrac{2}{3}\\\\\\
\Large\boxed{\boxed{\boxed{log_{ \tfrac{2}{3} } \dfrac{729}{64}=-6}}}.\\.

Tenha ótimos estudos ^^
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