SOLUTION: If log a base4=log b base8+1,find a relation between a and b without any logarithm.

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Question 1011616: If log a base4=log b base8+1,find a relation between a and b without any logarithm.
Answer by ikleyn(52887) About Me  (Show Source):
You can put this solution on YOUR website!
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If log a base4=log b base8+1,find a relation between a and b without any logarithm.
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log%284%2Ca%29 = 2%2Alog%282%2Ca%29,        <-----  is it clear to you? - It is because 4 = 2%5E2.

log%288%2Cb%29 = 3%2Alog%282%2Cb%29.        <-----  It is because 8 = 2%5E3.

Therefore  log%284%2Ca%29 = log%288%2Cb%29 + 1  (which is given) implies that

2%2Alog%282%2Ca%29 = 3%2Alog%282%2Cb%29 + 1,    or

a%5E2 = 2%2Ab%5E3.

It is the relation between a and b you are asked for.