Answer
$x\approx 6.0306$
Work Step by Step
\begin{align*}
\ln{x^3}+\ln5&=7 &\text{Power Property of logarithms}\\\\
\ln{(x^3\cdot 5)}&=7 &\text{Product Property of Logarithms.}\\\\
\ln{(5x^3)}&=7 \\\\
e^7&=5x^3 &\text{Write the equation in exponential form.}\\\\
\frac{e^7}{5}&=x^3&\text{Divide 5 to both sides.}\\\\
\sqrt[3]{\frac{e^7}{5}}&=\sqrt[3]{x^3}&\text{Take the cube root of both sides.}\\\\
x&=\sqrt[3]{\frac{e^7}{5}}\\\\
x&\approx 6.0306\end{align*}
Check:
\begin{align*}
3\ln{\left(\sqrt[3]{\frac{e^7}{5}}\right)}+\ln5&\stackrel{?}=7\\\\
7)&\stackrel{\checkmark}=7\end{align*}
Thus, the solution is $x=\sqrt[3]{\frac{e^7}{5}}\approx 6.0306$.
