Answer
$x\approx 4.780$
Work Step by Step
Use the Power Rule of logarithms to obtain:
\begin{align*}
\ln{x^3}-\ln2&=4
\end{align*}
Use the Quotient Rule of logarithms to obtain:
\begin{align*}
\ln{\left(\frac{x^3}{2}\right)}&=4
\end{align*}
Recall:
$$\ln{x}=n \longleftrightarrow e^n=x$$
Use the definition above to obtain:
\begin{align*}
e^4&=\frac{x^3}{2}\\\\
2(e^4)&=\frac{x^3}{4} \cdot 4\\\\
2e^4&=x^3\\\\
\sqrt[3]{2e^4}&=\sqrt[3]{x^3}\\\\
\sqrt[3]{2e^4}&=x\\\\
x&=\sqrt[3]{2e^4}\\\\
x&\approx 4.780\end{align*}
