# How do you solve 20 (100 - e^(x/2)) = 500?

Aug 6, 2015

$x = \log \left(5625\right) = 3.75$ 2 d.p.

#### Explanation:

Rearrange the expression as follows:

$20 \left(100 - {e}^{\frac{x}{2}}\right) = 500$ => ${e}^{\frac{x}{2}} = 75$

Take logarithms =f both sides:

$\log {e}^{\frac{x}{2}} = \frac{x}{2} = \log \left(75\right)$ => $x = 2 \log \left(75\right) = \log \left({75}^{2}\right) = \log \left(5625\right)$