Question

Resolva a equação logarítmica: log(2x) = log2 – log(8x)

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{log\:2x = log\:2 - log\:8x}$

$\mathsf{log\:2x = log\left(\dfrac{2}{8x}\right)}$

$\mathsf{2x = \dfrac{2}{8x}}$

$\mathsf{16x^2 = 2}$

$\mathsf{8x^2 = 1}$

$\mathsf{x = \pm\:\dfrac{1}{2\sqrt{2}}}$

$\mathsf{x = \pm\:\dfrac{1}{2\sqrt{2}}\:.\:\dfrac{\sqrt{2}}{\sqrt{2}}}$

$\mathsf{x = \pm\:\dfrac{\sqrt{2}}{4}}$

$\mathsf{S = \left\{\dfrac{\sqrt{2}}{4}\right\}}$