SOLUTION: prove the power property: log<sub>b</sub>U<sup>n</sup> = n·log<sub>b</sub>U

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Question 82835: prove the power property: logbUn = n·logbU
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

prove the power property: logbUn = n·logbU

Proof is by induction:

First we prove it's true for n = 1.

logbU1 = logbU = 1·logbU

Assume true for n < k,

Need to prove that logbUk+1 = (k+1)logbU

logbUk+1 = logb(UkU1) = logbUk + logbU1

= k·logbU + logbU =  (logbU)(k+1) = (k+1)logbU

Edwin