Question

log4 na base 8 - log2 na base √8

Answer 1

Resposta:

Explicação passo-a-passo:

$log_{8}4-log_{\sqrt{8}}2$ = x - y, sendo

log₈ 4 = x => 8ˣ = 4 => (2³)ˣ = 2² => 2³ˣ = 2² => 3x = 2 => x = 2/3

$log_{\sqrt{8}}2$ = y => $(\sqrt{8})^{y}=2=>(\sqrt{2^{3}})^{y}=2=>2^{\frac{3y}{2}}=2=>\frac{3y}{2}=1=>3y=2=>y=\frac{2}{3}$

Assim

$log_{8}4-log_{\sqrt{8}}2$ = x - y = 2/3 - 2/3 = 0