Answer
The value of x is 20.0855.
Work Step by Step
$6\ln x=18$
Simplify the logarithm $6\ln x=18$ as follows.
$\begin{align}
& 6\ln x=18 \\
& \ln x=3
\end{align}$
Use the fact that the expression ${{\log }_{a}}x=m\text{ is equivalent to }{{a}^{m}}=x$. Thus,
$\begin{align}
& x={{e}^{3}} \\
& \approx 20.0855
\end{align}$
Check:
Substitute $x=20.0855$ in the given equation.
$\begin{matrix}
6\ln \left( 20.0855 \right)\overset{?}{\mathop{=}}\,18 \\
\text{ }17.999\overset{?}{\mathop{=}}\,18 \\
\text{ }18\approx 18 \\
\end{matrix}$
Thus, the obtained solution is correct.
