Answer
$x=\ln3\approx1.098612$
Work Step by Step
$e^{2x}-e^{x}-6=0$
Let $e^{x}=u$ and $e^{2x}=u^{2}$ and rewrite the equation:
$u^{2}-u-6=0$
Solve by factoring:
$(u-3)(u+2)=0$
We get two solutions, which are:
$u=3$ and $u=-2$
Let's undo the initial substitution, knowing that $u=e^{x}$. The solutions then become:
$e^{x}=3$ and $e^{x}=-2$
Solve for $x$:
$x=\ln3\approx1.098612$
The other equation has no real solution.
