Question

If x² + y² = 6xy, prove that 2 log (x + y) = log x + log y + 3 log 2.

Answer 1

Given: x² + y² = 6xy 

x² + y² + 2xy = 6xy + 2xy 

(x + y)² = 8xy 

Taking logarithms on both sides log (x + y)² = log8xy 

⇒ 2log(x + y)= log8 + logx + logy [∵ logx^m = mlogx] 

[∵ logxy = logx + logy] 

= log2³ + logx + logy 

⇒ 2log(x + y) = logx + logy + 3log2