# How do you solve 2e^(3x) = 4e^(5x)?

##### 1 Answer
Jan 18, 2016

Start by dividing both sides by $4 {e}^{3 x}$ ...

#### Explanation:

$2 {e}^{3 x} = 4 {e}^{5 x}$

Divide both sides by $4 {e}^{3 x}$ ...

$\frac{1}{2} = {e}^{2 x}$

Now take the natural log of both sides ...

$\ln \left(\frac{1}{2}\right) = \ln \left({e}^{2 x}\right) = 2 x$

$x = \ln \frac{\frac{1}{2}}{2} = \frac{- \ln 2}{2} \approx - 0.3466$

hope that helped