Question

\[ \frac{e^{2y}-1}{e^{2y}+1} = x \]

How can we solve for e^y ?

Answer 1

First Cross Multiply

Answer 2

e^2y - 1 = x e^2y + x

e^2y - x e^2y = x + 1

e^2y ( 1-x) = x + 1

e^2y = (x+1) / (1-x)

e^2y = (e^y)^2

Take sqrt on both sides and u have e^y..:)

Answer 3

ie

e^y = sqrt [ (x+1) / (1-x) ]