# How do you solve for x in 7.316 = e^(ln(2x))?

Jul 6, 2016

$x = 3.658$

#### Explanation:

$\ln \left(x\right) = {\log}_{e} \left(x\right)$

The function $\ln \left(x\right) = a$ finds the value of a such that

$x = {e}^{a}$

Therefore, ${e}^{\ln \left(x\right)} = {e}^{a} = x$

What I'm trying to say is that ${e}^{x}$ and $\ln \left(x\right)$ are inverse operations, so they cancel out.

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

So $7.316 = 2 x \implies x = 3.658$