#### Answer

$x=-2$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given equation, $
\log_{10} 0.01=x
,$ use the properties of logarithms to find an equivalent expression for the logarithmic expression.
$\bf{\text{Solution Details:}}$
Using exponents, the value $0.01$ is equivalent to $10^{-2}.$ Hence, the equation above is equivalent to
\begin{array}{l}\require{cancel}
\log_{10} 10^{-2}=x
.\end{array}
Using the Power Rule of Logarithms, which is given by $\log_b x^y=y\log_bx,$ the equation above is equivalent to
\begin{array}{l}\require{cancel}
-2\log_{10} 10=x
.\end{array}
Since $\log_b b=1,$ the equation above is equivalent to
\begin{array}{l}\require{cancel}
-2(1)=x
\\\\
-2=x
\\\\
x=-2
.\end{array}