# How do you solve e^(x+6) = 4?

Jul 17, 2015

Take the natural logarithm of both sides, then subtract $6$ from both sides to find:

$x = {\log}_{e} \left(4\right) - 6 \cong - 4.6137$

#### Explanation:

Taking ${\log}_{e}$ of both sides we get:

${\log}_{e} \left(4\right) = {\log}_{e} \left({e}^{x + 6}\right) = x + 6$

Subtract $6$ from both ends to get:

$x = {\log}_{e} \left(4\right) - 6 \cong 1.3863 - 6 = - 4.6137$