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If a^2+b^2=7ab, then prove that "log"((a...

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

Text Solution

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`a^(2)+b^(2)= 7 ab`
` or (a+b)^(2) = 9 ab`
` or log(a+b)^(2) = log 9 ab`
` or 2 log(a+b) = 2log 3+log a+ log b`
` or 2(log(a+b)-log 3) = log a+ log b`
` or log((a+b)/3) =1/2 (log a+ log b)`
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