Question

(IME-RJ) Calcule o Logaritmo de 625 na base 5³√5.

Answer 1

log 625 = x
    $5^3\sqrt{5}$

$({5^3.5^\frac{1}{2}})^x=625$

$({5^\frac{7}{2}})^x = 5^4$

$5^\frac{7x}{2} = 5^4$

$\frac{7x}{2} = 4$

$7x = 8$

$x = \frac{8}{7}$

Answer 2

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{log_{\:5\sqrt[3]{5}}\:625 = x}$

$\mathsf{(5\sqrt[3]{5})^x = 625}$

$\mathsf{(5^x.5^{\frac{x}{3}}) = 5^4}$

$\mathsf{\not5^{\frac{4x}{3}} = \not5^4}$

$\mathsf{\dfrac{4x}{3}} = 4}$

$\mathsf{4x = 12}$

$\boxed{\boxed{\mathsf{x = 3}}}$