Hi,

My uncertainty lies in the approach to the question. Anyway, I made an attempt.

Given $\displaystyle \displaystyle e^x - e^{-x} = 4$, show that $\displaystyle \displaystyle x = \ln(2+\sqrt{5})$

$\displaystyle \displaystyle \ln e^x - \ln e^{-x} = \ln 4$

$\displaystyle \displaystyle x - (-x) = \ln 4$

$\displaystyle \displaystyle 2x = \ln 4$

$\displaystyle \displaystyle x = \ln 2$