Question

if log(x+y/3)=1/2(logx+logy),then find the value of x/y+y/x

Answer 1

given that
log(x+y/3) = 1/2(log x + log y)
log(x + y/3) = 1/2(log xy )
log(x+y/3) = log√xy
remove the log on the both sides 
(x+y/3) = √xy
(x+y/3)² = xy
(x+y)²/9 = xy                         ∴(x+y)² = x²+2xy+y²
x²+2xy+y² = 9xy
x²+y²= 9xy-2xy
x²+y² = 7xy  ---------------------------(1)

from the another
= x/y + y/x
= x² + y²/xy         from ----(1)
= 7xy / xy
= 7.