If X=loga(n), y=logc(n) where nis not equal to one . Prove that x-y/x+y=logb(c)-logb(a)/logb(c)+logb(a)

Answer 1

1/x = logn(a)
1/y = logn(c)

(x-y)/(x+y) = (1/y - 1/x)/(1/y + 1/x)
= logn(c/a)/logn(c*a)

logb(c)-logb(a) = logb(c/a)
logb(c)+logb(a) = logb(c*a)

The two ratios are equal.