How do you solve for x in 1000 = 20e^(x/4)?

Apr 9, 2016

$x = 15.648$

Explanation:

$1000 = 20 \cdot {e}^{\frac{x}{4}}$ or ${e}^{\frac{x}{4}} = \frac{1000}{20} = 50$

Taking log with base $e$ of both sides gives us,

$\frac{x}{4} = \ln 50 = 3.912$

and $x = 3.912 \times 4 = 15.648$