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

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Question 1043498: If a^2 + b^2=5 ab.prove that 2 log (a+b)=log 7+log a+log b
Found 2 solutions by Boreal, ikleyn:
Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website!
2 log (a+b)=log 7+log a+log b
log (a+b)^2=log (7ab)
raise to 10th power
(a+b)^2=7ab
a^2+2ab+b^2=7ab
but a^2+b^2=5ab
therefore, 5ab+2ab=7ab.

Answer by ikleyn(52848) (Show Source):
You can put this solution on YOUR website!
.
If a^2 + b^2=5 ab, then prove that 2 log (a+b)=log 7+log a+log b
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If = , then = (after adding 2ab to both side) = . Now take the logarithm of both sides (assuming a > 0, b > 0, which MUST be pointed in the condition, but mistakenly missed). You will get 2*log(a+b) = log(7) + log(a) + log(b), QED.

Solved.