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

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Answer 1 · 2016-07-06T11:50:49

See below

$log_a b = log_x a/(log_x b)$

so

$log_(b^n)(x^n)=log_ex^n/(log_e b^n) = (n log_e x)/(n log_e b) = (log_e x)/(log_e b) = log_b x$

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