Question

Se (2raiz de 2)elevado a x =64,qual o valor de logaritimo 1/8x?

Answer 1

x= e^ (2 raiz de 2) 1/8x = 1/8e^(2raiz de 2) Log(1/8x)= Log(1) / Log(8e^(2 raiz de 2) = Log(1) - Log(8e^(2 raiz de 2)= 0 - ( log(8) + ln(2 raiz de 2))

Answer 2

$(2\sqrt{2})^n = 64\\ (\sqrt{8})^n = 64\\\\ log_{\sqrt{8}}64=n\\ log_{\sqrt{8}}64=4$

Prova Real:
$(\sqrt{8})^4 = 64\\ (8)^2 = 64\\ \boxed{64 = 64}$

Bons estudos!