SOLUTION: a and b is positive integer.how could you get solution this equation? 3power a -7 power b=0

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Question 171132: a and b is positive integer.how could you get solution this equation?
3power a -7 power b=0
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
a and b is positive integer.how could you get solution this equation?
3power a -7 power b=0
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3%5Ea+=+7%5Eb
log%283%5Ea%29+=+log%287%5Eb%29
a*log(3) = b*log(7)
a/b = log(7)/log(3) =~ 1.7712
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It's difficult, and maybe impossible, to prove that there are no 2 integers with that ratio.
However, it is not possible to find a and b that satisfy the given conditions except a = b = 0.
3 to any integer power will have factors of only 3's, no 7's, and vice versa.