# Question #814a5

Jun 15, 2016

$x = {\log}_{e} 2$

#### Explanation:

Make ${e}^{x} = y$ then solve for $y$ the resulting equation

$y + 12 = {y}^{2}$

giving $y = \left\{- 3 , 2\right\}$.

Analyzing those solutions we choose $y = 2$ because $y = - 3 = {e}^{x}$ is inconsistent. Remember that ${e}^{x} > 0$ always. Then if ${e}^{x} = 2 \to x = {\log}_{e} 2$