# How do you prove log_(b^n)(x^n)=log_(b)x?

${\log}_{a} b = {\log}_{x} \frac{a}{{\log}_{x} b}$
${\log}_{{b}^{n}} \left({x}^{n}\right) = {\log}_{e} {x}^{n} / \left({\log}_{e} {b}^{n}\right) = \frac{n {\log}_{e} x}{n {\log}_{e} b} = \frac{{\log}_{e} x}{{\log}_{e} b} = {\log}_{b} x$