Question

If x^4 + y^4 =83x^2y^2 then prove that log (x^2/9-y^2/9)= log x+ logy

Answer 1

x^4 + y^4 = 83x^2y^2

x^4+y^4-2x^2y^2= 83x^2y^2

x^4-2x^2y^2+y^4= 81x^2y^2

(x^2-y^2)^2= 81x^2y^2

x^2-y^2= 9xy

log(x^2-y^2)= log(xy)

log(x^2-y^2)= log 9+ logxy

log(x^2-y^2)-log 9= logxy

log (x^2/9-y^2/9)= logy