Question

log√8(1/64) qual é o resultado?

Answer 1

Resposta:

$\text{\sf Leia abaixo}$

Explicação passo-a-passo:

$\sf log_{\sqrt{8}}\:\dfrac{1}{64}$

$\sf log_{8^{\frac{1}{2}}}\:8^{-2}$

$\sf \left(8^{\frac{1}{2}}\right)^x = \left(8\right)^{-2}$

$\sf \not8^{\frac{x}{2}} = \not8^{-2}$

$\sf \dfrac{x}{2} = -2$

$\sf x = -4$

$\boxed{\boxed{\sf log_{\sqrt{8}}\:\dfrac{1}{64} = -4}}$

Answer 2

Explicação passo-a-passo:

$\sf log_{\sqrt{8}}~\dfrac{1}{64}=x$

$\sf (\sqrt{8})^x=\dfrac{1}{64}$

$\sf (\sqrt{2^3})^x=2^{-6}$

$\sf (2^{\frac{3}{2}})^x=2^{-6}$

$\sf 2^{\frac{3x}{2}}=2^{-6}$

Igualando os expoentes:

$\sf \dfrac{3x}{2}=-6$

$\sf 3x=2\cdot(-6)$

$\sf 3x=-12$

$\sf x=\dfrac{-12}{3}$

$\sf \red{x=-4}$