Question

How do you show that `tanh^-1(x) = (1/2) ln ((1+x)/(1-x))`?

Answer 1

Let `y=tanh^(-1)x`. Then `x = tanh y = (e^y-e^(-y))/(e^y+e^(-y))=(e^(2y)-1)/(e^(2y)+1)`.. Solving for `e^(2y)` and then for y, by equating logarithms, we get the logarithmic form.

Explanation:

Note that I had corrected the question by changing 'x-1' to '1-x'.