Solve the exponential equation below. Express irrational solutions in exact form and as a decimal rounded to 3 decimal places.
[e^(x) - e^(-x)]/2 = -2
$\displaystyle \frac{e^x - e^{-x}}{2} = -2$
multiply both sides by 2 ...
$\displaystyle e^x - e^{-x} = -4$
multiply every term by $\displaystyle e^x$ ...
$\displaystyle (e^x)^2 - 1 = -4e^x$
$\displaystyle (e^x)^2 + 4e^x - 1 = 0$
let $\displaystyle u = e^x$
$\displaystyle u^2 + 4u - 1 = 0$
use the quadratic formula to solve for u, then use the natural log (ln) to solve for x.