\begin{notes}
Note the properties:

$$\ln (x \cdot y) = \ln (x) + \ln (y)$$ and
$$e^a \cdot e^b = e^{a+b}$$
\end{notes}

\begin{xmpl}

Solve the equation $$10e^{1/3x} + 3 = 24$$ for $x$.

First, get the 3 out of the way.

 $$10e^{1/3x} = 21$$

Then the 10.

$$e^{1/3x} = 2.1$$

Next, we can take the natural log of 2.1. Since $ln$ is an inverse function of $e$ this would result in

$$\frac{1}{3}x = \ln(2.1)$$

This yields $$x = \ln(2.1) \cdot 3$$ which is $$\approx 2.23$$
\end{xmpl}