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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)`

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`a^2+b^2=7abimpliesa^2+b^2+2ab=9ab`
`implies(a+b)^2=9ab`
`implies((a+b)/3)^2=abimplies2"log"_2((a+b)/3)=("log"_2a+"log_2b)`
`implies"log"_2((a+b)/3)=1/2("log"_2a+"log"_2b)`
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