# How do you solve 14e^(3x+2)=560?

Dec 7, 2015

$x = \frac{\ln 40 - 2}{3}$

#### Explanation:

If
$\textcolor{w h i t e}{\text{XXX}} 14 {e}^{3 x + 2} = 560$
then (after dividing both sides by $14$)
$\textcolor{w h i t e}{\text{XXX}} {e}^{3 x + 2} = 40$

By taking the natural logarithm of both sides:
$\textcolor{w h i t e}{\text{XXX}} 3 x + 2 = \ln 40$

$\textcolor{w h i t e}{\text{XXX}} 3 x = \ln 40 - 2$

$\textcolor{w h i t e}{\text{XXX}} x = \frac{\ln \left(40\right) - 2}{3}$