Question

Determine o valor do logaritmo:

$log_{5 \sqrt[3]{5} }625$

Answer 1

$log_{5 \sqrt[3]{5}}625=x\\ \\ (5 \sqrt[3]{5})^x=625\\ \\ (5*5^{\frac{1}{3}})^x=5^4\\ \\ 5^{\frac{4}{3}x}=5^4\\ \\ \frac{4x}{3}=4\\ \\ 4x=12\\ \\ x=\frac{12}{4}=3$

Answer 2

$log_5 _(\sqrt[3]{5})\ 625 =x\\\\ (5 \sqrt[3]{5})^x = 625\\\\ 5*5^\frac{1}{3}^x=5^4\\\\ 5^\frac{4x}{3} = 5^4\\\\ \frac{4x}{3} = 4\\\\ 4x = 12\\\\ x=\frac{12}{4}\\\\ \boxed{x=3}$