Question

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

Answer 1

See below

Explanation:

`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`