Question

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

Answer 1

Check the attachment 

Answer 2

Answer 7

Explain:log (x+y÷3)=½(logx+logy)

2×log(x+y)=logx+logy

Log(x+y÷3)²=logxy

Remove log from both sides

(x+y/3)²=xy

(x+y)²/3²=xy

X²+y²+2xy=9xy

x²+y²=9xy-2xy

x²+y²=7xy

Divide both sides with xy

x²/xy+y²/xy=7xy/xy

x/y+y/x=7