# How do you solve 2e^(5x+2) = 8?

##### 1 Answer
Oct 22, 2015

$x = \frac{1}{5} \left(\ln 4 - 2\right)$

$= - 0 , 1227411$

#### Explanation:

Using laws of exponents and rearranging we may write this as

${e}^{5 x} \cdot {e}^{2} = \frac{8}{2}$

Now taking the natural logarithm on both sides and using laws of logs we get

$5 x = \ln \left(\frac{4}{{e}^{2}}\right)$

$\therefore x = \frac{1}{5} \left(\ln 4 - 2\right)$

$= - 0 , 1227411$