SOLUTION: how do you to the log base 2 of the third root of 32. if you could explain too

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Question 98950: how do you to the log base 2 of the third root of 32. if you could explain too
Answer by Edwin McCravy(20067) About Me  (Show Source):
You can put this solution on YOUR website!
how do you to the log base 2 of the third root of 32.
if you could explain too


               log2root%283%2C32%29

Rewrite root%283%2C32%29 as 32%5E%281%2F3%29

               log232%5E%281%2F3%29

Break 32 into prime factors:  32 = 2򈭾򈭾 = 2%5E5
then replace 32 by 2%5E5

               log2%282%5E5%29%5E%281%2F3%29

Remove the parentheses by multiplying the inner exponent 5
by the outer exponent 1%2F3 to get 5%2F3

               log22%5E%285%2F3%29

Use the principle logbb%5En%29 = n

               5%2F3

That's the answer. 

Edwin