Question

Resolva as equações a seguir: a) log(3) (x-2) - log(9) (x-2) =2

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{log_3\:(x - 2) - log_9\:(x - 2) = 2}$

$\mathsf{log_3\:(x - 2) - log_{3^2}\:(x - 2) = 2}$

$\mathsf{log_3\:(x - 2) - \dfrac{1}{2}\:log_3\:(x - 2) = 2}$

$\mathsf{2\:log_3\:(x - 2) - log_3\:(x - 2) = 2.2}$

$\mathsf{log_3\:(x - 2)^2 - log_3\:(x - 2) = log_3\:3^4}$

$\mathsf{log_3\:\dfrac{(x - 2)^2}{(x - 2)} = log_3\:81}$

$\mathsf{log_3\:(x - 2) = log_3\:81}$

$\mathsf{x - 2 = 81}$

$\boxed{\boxed{\mathsf{x = 83}}}$