Question

Resolvendo a equação abaixo, qual o valor de x?

$5log(\frac{x}{8})+2log(\frac{x}{5})=4log(x)-log(25)$

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\sf 5\:.\:log\left(\dfrac{x}{8}\right) + 2\:.\:log\left(\dfrac{x}{5}\right) = 4\:.\:log\:x - log\:25$

$\sf log\left(\dfrac{x}{8}\right)^5 + log\left(\dfrac{x}{5}\right)^2 = log\:x^4 - log\:25$

$\sf log\left(\dfrac{x^5\:.\:x^2}{8^5\:.\:5^2}\right) = log\left(\dfrac{x^4}{25}\right)$

$\sf \left(\dfrac{x^5\:.\:x^2}{8^5\:.\:5^2}\right) = \left(\dfrac{x^4}{25}\right)$

$\sf \dfrac{x^3}{8^5} = 1$

$\sf x = \sqrt[\sf 3]{\sf 8^3\:.\:4^3}$

$\boxed{\boxed{\sf x = 32}}$