SOLUTION: If a^2 + b^2 =14ab, prove that log ((a+b)/4) = 1/2 (log a+log b )

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Question 685554: If a^2 + b^2 =14ab, prove that log ((a+b)/4) = 1/2 (log a+log b )
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!

a%5E2+%2B+b%5E2+=+14ab
Add 2ab to both sides
a%5E2+%2B2ab+%2Bb%5E2=16ab
perfect square
%28a%2Bb%29%5E2=16ab
%281%2F16%29%28a%2Bb%29%5E2=ab
Take log on both sides
log%28%28%281%2F16%29%28a%2Bb%29%5E2%29%29=log%28%28ab%29%29
2log%28%28%281%2F4%29%28a%2Bb%29%29%29=log%28%28ab%29%29