## Precalculus (6th Edition) Blitzer

$x\approx 1.10$
$e^{2x}-e^{x}-6=0$ introduce a temporary variable, $t=e^{x}$ and the equation is equivalent to $t^{2}-t-6=0\quad$ ... factor the trinomial $(t+2)(t-3)=0$ Either $t=-2$ or $t=3$ Bring back x: Either $e^{x}=-2$ or $e^{x}=3$ $e^{x}$ is never negative, so it can't be that $e^{x}=-2$ This leaves: $e^{x}=3\qquad$ ... apply $\ln$( ) to both sides $x=\ln 3\qquad$... use calculator and round to two decimal places $x\approx 1.10$