Question

2 log(x+y)=2log 5+log x+log y find x/y+y/x

Answer 1

log(x+y)^2=log5^2+log(xy)

log(x+y)^2=log(25xy)

taking antilog both side .

we get,

(x+y)^2=25xy

by opening the brackets

x^2+y^2+2xy=25xy

so x^2+y^2=23xy----(1)

and we have to find x/y+y/x=(x^2+y^2)/xy

and from equation (1) we know the value of x^2+y^2=23xy

so x/y+y/x=23xy/xy=23.

hope these will help you

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