Answer
$x=\dfrac{1}{100}$
Work Step by Step
Since $\log_b y=x$ implies $b^x=y,$ the given equation, $
\log x=-2
,$ is equivalent to
\begin{align*}
\log_{10} x&=-2
&(\log x=\log_{10} x)
\\
10^{-2}&=x
\\\\
\dfrac{1}{10^2}&=x
&(a^{-m}=\dfrac{1}{a^m})
\\\\
\dfrac{1}{100}&=x
.\end{align*}
Hence, the solution to the equation $\log x=-2$ is $x=\dfrac{1}{100}$.
