Question 777869
x^2+y^2=10xy

x^2+2xy+y^2=10xy+2xy

(x+y)^2= 10xy+2xy

(x+y)^2=12xy

x^2+y^2=10xy

x^2-2xy+y^2=10xy-2xy

(x-y)^2=8xy


2 log ( x+y/x-y)=log 3/2

LHS 
2 log ( x+y/x-y)

log((x+y)/(x-y))^2

=log((x+y)^2/(x-y)^2)

=log (12xy/8xy)

= log3/2=RHS