Question

If $x^2+y^2=7xy$ then show that $2\log (x+y)=\log x+\log y+2\log 3$.

Answer 1

$x^2+y^2=7xy(a+b{)}^2=a^2+b^2+2ab(x+y{)}^2-2xy=7xy(x+y{)}^2=9xy\log (x+y{)}^2=\log \left(9xy\right)$

Using logarithm properties

$2\log \left(x+y\right)=\log \left(x\right)+\log \left(y\right)+2\log 3$

Hence Proved