Question

considere k, m € IR com m ›1 e x ≠ k.calcule x em função de k e m,sabendo que log (x² - K²)=10 e log m (x + k) = 1/3​

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\begin{cases}\mathsf{log\:(x^2 - k^2) = 10}\\\mathsf{log_m\:(x + k) = \dfrac{1}{3}}\end{cases}$

$\mathsf{x^2 - k^2 = 10^{10}}$

$\mathsf{(x + k).(x - k) = 10^{10}}$

$\mathsf{(x + k) = \sqrt[3]{\textsf{m}}}$

$\mathsf{(\sqrt[3]{\textsf{m}}).(x - k) = 10^{10}}$

$\mathsf{x - k = \dfrac{10^{10}}{\sqrt[3]{\textsf{m}}}}$

$\boxed{\boxed{\mathsf{x = \dfrac{10^{10}}{\sqrt[3]{\textsf{m}}} + k}}}$