Question

Calcule o valor da expressão abaixo ↓
Por favor, me ajudem, é pra hoje...

Answer 1

A forma mais facil aqui é calcular os logaritmos separados e depois substituir na expressão.

$log_{_3}1=a\\\\1=3^a\\\\3^0=3^a\\\\a=0$

$log0,01\\\\log\frac{1}{100}\\\\log\frac{1}{10^2}\\\\log1+log10^2\\\\log1+2log10\\\\0+2\;.\;1\\\\2$

$log_{_2}\frac{1}{64}=b\\\\log_{_2}\frac{1}{2^6}=b\\\\log_{_2}1-log_{_2}2^6=b\\\\0-6.log_{_2}2=b\\\\log_{_2}2=\frac{b}{-6}\\\\2=2^{\frac{b}{-6}}\\\\\frac{b}{-6}=1\\\\b = -6\;.\;1\\\\b=-6$

$log_{_4}\sqrt{8}=c\\\\log_{_4}\sqrt{2^3}=c\\\\log_{_4}2^{\frac{3}{2}}=c\\\\2^{\frac{3}{2}}=4^c\\\\2^{\frac{3}{2}}=2^{2^c}\\\\2^{\frac{3}{2}} = 2^{2c}\\\\2c=\frac{3}{2}\\\\c = \frac{3}{4}$

Juntando as informações na expressão:

$\frac{0 \;+\;2 }{-6\;.\;\frac{3}{4}}\\\\\frac{2}{\frac{-18}{4}}\\\\-\frac{2\;.\;4}{18}\\\\-\frac{4}{9}$