$\displaystyle cosh^{-1}x=ln(x+\sqrt{x^2-1}), x>=1$

I need to derive the formula above by using the definition of cosh (which I think is below) and then solving for the inverse

$\displaystyle cosh x = \frac{e^{-x} + e^x}{2}$

How do I get the e^-x and e^x to join to create like 1 variable so I can solve for the inverse?