if a square + b square=7ab, prove log 1/3 (a+b)=1/2 (log a +log b)

if a square + b square=7ab, prove log 1/3 (a+b)=1/2 (log a +log b)

thanks in advance.

(no silly answers pls)
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1 Answer

½(log(a)+log(b))=½log(ab)=log√(ab).

If log(⅓(a+b))=log√(ab), then:

⅓(a+b)=√(ab),

a+b=3√(ab),

a²+2ab+b²=9ab,

a²+b²=7ab.

So the two equations are equivalent. QED.

by Top Rated User (1.2m points)

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