Answer
$x=\ln 3\approx 1.0986$
Work Step by Step
We need to solve:
$e^{2x}-e^{x}-6=0$
We factor:
$(e^{x}-3)(e^{x}+2)=0$
$e^{x}+2=0$ or $e^{x}-3=0$
$e^x=-2$ or $e^x=3$
$x=\ln(-2)=$ no solution or $x=\ln 3\approx 1.0986$
(The left equation has no solution because we can't take a log of a negative number.)