# How do you solve 2e^(0.5x)=45?

Jul 29, 2016

$x = 6.227$

#### Explanation:

As $2 {e}^{0.5 x} = 45$, we have

${e}^{0.5 x} = \frac{45}{2} = 22.5$.

Hence $0.5 x = \ln 22.5$ and

$x = \ln \frac{22.5}{0.5} = \ln \frac{22.5}{\frac{1}{2}} = 2 \times \ln 22.5 = 2 \times 3.1135 = 6.227$