Question

if x²+y²=6xy prove that 2log(x+y)=log x +log y +3log2​

Answer 1

Given that,

x² + y² = 6xy

or, (x + y)² - 2xy = 6xy

or, (x + y)² = 8xy

or, (x + y)² = 2³xy

Taking (log) in both sides, we get

log (x + y)² = log (2³xy)

or, 2 log (x + y) = log (2³) + logx + logy

or, 2 log (x + y) = 3 log2 + logx + logy

Hence, proved.

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