The power property of logarithms, which we 
are to prove, is

(1)   

But first we prove this: 

(2)     

-----------------

Let 

Then by definition of logarithm



Substitute for x



So we have proved (2).

-----------------

Let 

Then by the definition of logarithm:



Using (2) to replace A



Use the rule of multiplying 
exponents on the right:



Equate the powers of B



Since 



So we have proved (1)

Edwin