Given that x^2 + y^2 = 6xy, find an equivalent expression to 2 log(x+y).

2log(x+y)

= log[(x+y)^2]

= log[x^2 +2xy +y^2] ------------(i)

x^2 +y^2 = 6xy

Add 2xy to both sides,

x^2 +2xy +y^2 = 8xy

(x +y)^2 = 8xy

So,

2log(x+y)

= log(8xy) --------------answer.

Or,

= log(8) +log(x) +log(y)

= log(2^3) +log(x) +log(y)

= 3log(2) +log(x) +log(y) -------------answer also.