Question

Qual o logaritmo de 4 na base 1/8?

Answer 1

$log_{\frac{1}{8}}4=x \Rightarrow (\frac{1}{8})^x=4\\ \\ 2^{-3x}=2^2\\ \\ -3x=2\\ \\ \boxed{x=-\frac{2}{3}}$

Answer 2

$log_ba=x-->b^x=a \\ \\ log_ \frac{1}{8}4=x \\ (\frac{1}{8})^x=4 \\ (2^{-3})^x=2^2 \\ 2^{-3x}=2^2 \\ -3x=2 \\ 3x=-2 \\ x= \frac{-2}{3} \\ \\log_ \frac{1}{8}4= \frac{-2}{3}\\\\\\Renato.$