​ If x + y = 7xy, then prove that log (x+y /3) = 1/2 (log x + log y). ​

Question

If x + y = 7xy, then prove that log (\(\frac{x+y}{3}\)) = 1/2 (log x + log y).

Answer 1

Given x² + y² = 7xy now add (2xy) on both sides. 

We get 

x² + y² + 2xy = 7xy + 2xy = 9xy 

Considering square root on both sides 

we get