Question

a soluçao da equaçao logaritmica log^4 x-log^8 x=1 e: a) {2} b) {24} c) {42} d){64} e) {106}

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{log_4\:x - log_8\:x = 1}$

$\mathsf{log_{2^2}\:x - log_{2^3}\:x = 1}$

$\mathsf{\dfrac{1}{2}\:log_{2}\:x - \dfrac{1}{3}\:log_{2}\:x = 1}$

$\mathsf{log_{2}\:x^3 - log_{2}\:x^2 = 6}$

$\mathsf{log_{2}\:\dfrac{x^3}{x^2} = log_2\:64}$

$\mathsf{\dfrac{x^3}{x^2} = 64}$

$\boxed{\boxed{\mathsf{x = 64}}}\leftarrow\textsf{letra D}$