How do you solve 5e^(2x) = 500?

Apr 29, 2018

$x = \ln \frac{100}{2}$

Explanation:

We can start off by dividing both sides by $5$. We get

${e}^{2 x} = 100$

We can take the natural log of both sides to cancel out base $e$. We get

$\ln \left({e}^{2 x}\right) = \ln \left(100\right)$

$\implies 2 x = \ln \left(100\right)$

$x = \ln \frac{100}{2}$

I chose to not evaluate $\ln \left(100\right)$ so we could get an exact answer, but it will evaluate to about $4.6$, and dividing it by $2$ would give us about $2.3$.

Hope this helps!