Question

The question is below?

If `n=(a^x-a^(-x))/(a^x+a^(-x))` then find `log_a((1+n)/(1-n))`. Ans=2n

Answer 1

`n=(a^x-a^(-x))/(a^x+a^(-x))`

`1 + n = (a^x+a^(-x) + a^x-a^(-x))/(a^x+a^(-x)) = (2a^x)/(a^x+a^(-x))`

`1 - n = (a^x+a^(-x) - a^x + a^(-x))/(a^x+a^(-x)) = (2a^(-x))/(a^x+a^(-x))`

`(1+n)/(1-n) = (2a^x)/ (2a^(-x))=a^{2x}`

`log_a((1+n)/(1-n)) = 2 x`