Answer
$x=\ln2\approx0.693147$ and $x=0$
Work Step by Step
$e^{2x}-3e^{x}+2=0$
Let $e^{x}=u$ and $e^{2x}=u^{2}$ and rewrite the equation:
$u^{2}-3u+2=0$
Solve by factoring:
$(u-2)(u-1)=0$
We get two solutions, which are:
$u=2$ and $u=1$
Let's undo the initial substitution, knowing that $u=e^{x}$. The solutions become:
$e^{x}=2$ and $e^{x}=1$
Solve for $x$ in both equations:
$x=\ln2$ and $x=0$
Our two final solutions are:
$x=\ln2\approx0.693147$ and $x=0$
