Answer
The value of x is 0.0498.
Work Step by Step
Consider the logarithmic equation.
$2\ln x=-6$
Simplify the logarithm $2\ln x=-6$ as follows.
$\begin{align}
& 2\ln x=-6 \\
& \ln x=-3
\end{align}$
Use the fact that the expression ${{\log }_{a}}x=m\text{ is equivalent to }{{a}^{m}}=x$. Therefore,
$\begin{align}
& x={{e}^{-3}} \\
& \approx 0.0498
\end{align}$
Check:
Substitute $x=0.0498$ in the given equation.
$\begin{matrix}
2\ln \left( 0.0498 \right)\overset{?}{\mathop{=}}\,-6 \\
\text{ }2\left( -3 \right)\overset{?}{\mathop{=}}\,-6 \\
\text{ }-6=-6 \\
\end{matrix}$
Thus, the obtained solution is correct.
