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

Mar 6, 2018

$\approx - 0.2554128119$

#### Explanation:

The laws of logarithms state that:

1) ${\log}_{a} {b}^{c} = c {\log}_{a} b$

2) ${\log}_{a} a = 1$

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

Divide by $5$:

${e}^{2 x} = \frac{3}{5}$

Taking natural logarithms of both sides:

$2 x \ln e = \ln \left(\frac{3}{5}\right) \textcolor{w h i t e}{8888}$ by 1

By 2:

$2 x \left(1\right) = \ln \left(\frac{3}{5}\right)$

Divide by 2:

$x = \ln \frac{\frac{3}{5}}{2} \approx - 0.2554128119$