Question

Determine o logaritmo de raiz de 5 na base 125

Answer 1

$log_{125} \ \sqrt{5}=x \Leftrightarrow 125^x= \sqrt{5} \\ \\ 125^x = \sqrt{5}, \ \ \ \ 125^x = (5^3)^x = 5^{3x} \ \ \ \& \ \ \ \sqrt{5}=5^{ \frac{1}{2} }, \ \ \ entao:$

$log_{125}\ \sqrt{5}=x \Leftrightarrow 5^{3x}=5^{ \frac{1}{2} } \Leftrightarrow 3x = \frac{1}{2} \Leftrightarrow x = \frac{3}{2}$

$Logo\ \ x = \frac{3}{2}$