# How do you solve e^ { x + 4} = \frac { 1} { e ^ { 6} }?

Apr 24, 2017

$x = - 10$

#### Explanation:

Ideally, we want it in the form ${e}^{x + 4} = {e}^{\text{some number}}$. We have to rewrite $\frac{1}{e} ^ 6$ somehow.

Luckily, we can change the sign of the exponent in order to write it in the numerator:

${e}^{x + 4} = \frac{1}{{e}^{6}}$

${e}^{x + 4} = {e}^{- 6}$

Now we can compare exponenents:

$x + 4 = - 6$

Solve for $x$

$x = - 10$