SOLUTION: What is log 2 to base 64 divided by log 5 to base 125

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Question 1055184: What is log 2 to base 64 divided by log 5 to base 125
Found 2 solutions by josmiceli, Boreal:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+log%28+64%2C+2+%29++=+1%2F6+
( this is because the 6th root of +64+
is +2+ )
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+log%28+125%2C+5+%29+=+1%2F3+
( the 3rd root of +125+ is +5+ )
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+log%28+64%2C2+%29+%2F+log%28+125%2C+5+%29+=+%28%28+1%2F6+%29%29+%2F+%28%28+1%2F3+%29%29+
+%28%28+1%2F6+%29%29+%2F+%28%28+1%2F3+%29%29+=+1%2F2+

Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
log(64) (2)/log(125)5=
(1/6)/(1/3)=(1/2)
One may use the change of base formula, but here recognizing that 2^6=64 so 64^(1/6)=2 speeds things up. Similarly, 125^(1/3)=5.