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

1 Answer

Jul 6, 2016

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#

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