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

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.