Correct question is: 

If log[(x + y)/3] = 1/2(log x + log y), then find the value of x/y + y/x

Solution:

Given, log [( x + y)/3] = 1/2(log x + log y)

=> 2 * log[( x + y)/3] = log x + log y

=> log[( x + y)/3]² = log xy

Removing log on both sides, we get

     [( x + y)/3]² = xy

=> ( x + y )² /3² = xy

=> (x² + y² + 2xy)/9 = xy

=> x² + y² + 2xy = 9xy

=> x² + y² = 9xy - 2xy

=> x² + y² = 7xy

Divide each term with xy, we get

     x² / xy + y² / xy = 7xy / xy

=> x/y + y/x = 7

So, the value of x/y + y/x is 7