Hi All, please see if my steps are alright below:

Solve for x

$\displaystyle e^{2x} - 7e^x + 12$

$\displaystyle e^{2x} - 7e^x = -12$

$\displaystyle e^{2x} - (e^x)^{7} = -12$

$\displaystyle ln(\frac{e^{2x}}{e^(7x)} = e^{-12}$

$\displaystyle ln(e^{-5x} = e^{-12}$

$\displaystyle -5x = -12 \rightarrow x = \frac{12}{5}$