SOLUTION: If a^2+b^2=7ab prove that 2 log(a-b)=log 5+log a+log b

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Question 1043490: If a^2+b^2=7ab prove that 2 log(a-b)=log 5+log a+log b
Answer by ikleyn(52812) About Me  (Show Source):
You can put this solution on YOUR website!
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If a^2 + b^2=7 ab, then prove that 2 log (a-b)=log 5+log a+log b
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If a%5E2+%2B+b%5E2 = 7ab, then

a%5E2+-+2ab+%2B+b%5E2 = 7ab+-+2ab    (after adding 2ab to both side)

%28a+-+b%29%5E2 = 5ab.

Now take the logarithm of both sides (assuming a > b > 0, which MUST be pointed in the condition, but mistakenly missed).
You will get

2*log(a-b) = log(5) + log(a) + log(b).   QED.

Solved.