Answer
The value of x is $\frac{1}{1000}$.
Work Step by Step
$\log x=-3$
Simplify the logarithm $\log x=-3$ as follows.
$\log x=-3$
Use the fact that the expression ${{\log }_{a}}x=m\text{ is equivalent to }{{a}^{m}}=x$. Therefore,
$\begin{align}
& x={{10}^{-3}} \\
& =\frac{1}{{{10}^{3}}} \\
& =\frac{1}{1000}
\end{align}$
Check:
Substitute $x=\frac{1}{1000}$ in the given equation.
$\begin{matrix}
\log \left( \frac{1}{1000} \right)\overset{?}{\mathop{=}}\,-3 \\
\text{ }-3=-3 \\
\end{matrix}$
Thus, the obtained solution is correct.
