Question

S= log 1/2 8 - log 4/3 27/64 - log(2) 1024

Answer 1

Boa tarde Garoto!

Solução!

Vamos resolver os logaritmos separados,e em seguida subtrair os seus valores

.$S=log_{ \frac{1}{2}}8-log_{ \frac{4}{3} } \frac{27}{64}-log_{2}1024$

$log_{ \frac{1}{2}}8 \\\\ 8= (\frac{1}{2})^{x} =2^{3}=2^{-x} = x=-3 \\\\\\ log_{ \frac{4}{3} } \frac{27}{64}\\\\\ ( \frac{27}{64} )=( \frac{4}{3})^{x} \\\\\ ( \frac{3}{4})^{3}= ( \frac{4}{3} )^{x} \\\\\ ( \frac{4}{3})^{-3} =( \frac{4}{3})^{x}\\\\ x=-3 \\\\\\ log_{2}1024 \\\\\ 1024=2^{x} \\\\\ 2^{10}=2^{x} \\\\\ x=10$

$S=-3-(-3)-10 \\\\ S=-3+3-10\\\\ S=-10$

Bons estudos!