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If a^2+ b^2=7ab, prove that log(1/3 (a+ ...

If `a^2+ b^2=7ab`, prove that `log(1/3 (a+ b)) =1/2 (log a+ log b)`

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`a^2+b^2=7ab`
adding 2ab on both sides
`a^2+b^2+2ab=7ab+2ab`
`(a+b)^2=9ab`
`(a+b)=3sqrt(ab)`
`(a+b)/3=(ab)^(1/2)`
taking log both sides
`log((a+b)/3)=log(ab)^(1/2)`
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