Question

if x square + y square =6xy 2log (x+y)= logx+logy+3log2

Answer 1

x²+y² = 6xy

Adding 2xy on both sides,
x²+y²+2xy = 6xy+2xy
(x+y)² = 8xy

Take logarithm on both sides,
log(x+y)² = log 8xy
2log (x+y) = log 8 + log x + log y
2log (x+y) = log 2³ + log x + log y
2log (x+y) = 3log2 + log x + log y

Hence proved!

Formula used :
log aⁿ = n log a
log mn = log m + log n

Hope it helps