I recently took my Honors Pre-Calc. exam. Wanting to get as many points as I possibly could, I circled and skipped several problems. However, I forgot to do this one, and wanted to know if I'm on the right track, because the answer I get for x doesn't work correctly. I've come up with a separate solution that comes close, but is off by .4 as well.
\begin{align*}
e^{2x} - 7e^x + 12 &= 0\\
e^{2x} - 7e^x &= -12 \\
e^x(1^2 - 7) &= -12\\
e^x &= \frac{-12}{1^2 - 7}\\
e^x &= 2\\
x &= \ln 2
\end{align*}
Putting this back into the equation doesn't work. I think I might have a problem with how I'm factoring, but I can't seem to fix it. The only other way I've tried comes closer, but still gives me a wrong answer.
Your help and suggestions are appreciated :).