Answer
$-2$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the properties of logarithms to simplify the given expression, $
\log 0.01
.$
$\bf{\text{Solution Details:}}$
The given expression is equivalent to
\begin{array}{l}\require{cancel}
\log \dfrac{1}{100}
\\\\=
\log \dfrac{1}{10^2}
.\end{array}
Using the Quotient Rule of Logarithms, which is given by $\log_b \dfrac{x}{y}=\log_bx-\log_by,$ the expression above is equivalent
\begin{array}{l}\require{cancel}
\log 1-\log 10^2
.\end{array}
Using the Power Rule of Logarithms, which is given by $\log_b x^y=y\log_bx,$ the expression above is equivalent
\begin{array}{l}\require{cancel}
\log 1-2\log 10
.\end{array}
Since $\log_b1=0$ and $\log_b b=1,$ the expression above is equivalent
\begin{array}{l}\require{cancel}
\log 1-2\log_{10} 10
\\\\=
0-2(1)
\\\\=
0-2
\\\\=
-2
.\end{array}