SOLUTION: Prove that {{{log(B,a^x) = x*log(B,a)}}}

Let  equal the left side

 

Let  equal the right side



Take the first equation:



By definition of logarithms,



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Take the second equation:



Divide both sides by x



By definition of logarithms,



Raise both sides to the x power





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So we have the two equations:




Therefore

 since both equal to 

Therefore if B is positive and not equal to 1. then



Therefore



Edwin