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If `a^(2)+b^(2)=23ab`, then prove that `log(a+b)/5=1/2(loga+logb)`

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If `a^(2)+b^(2)=23ab`, then prove that `log(a+b)/5=1/2(loga+logb)`
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`a^(2)+b^(2)=(a+b)^(2)-2ab = 23 ab`
`rArr (a+b)^(2)=25ab rArr a+b = 5sqrt(ab)` ……….(i)
LHS `=log(a+b)/5 = log(5sqrt(ab))/5 = 1/2logab = 1/2(loga +logb)`=RHS
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