Answer
$x=-3$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given equation, $
x=\log_{10} 0.001
,$ use the properties of logarithms to find an equivalent expression for the logarithmic expression.
$\bf{\text{Solution Details:}}$
Using exponents, the value $0.001$ is equivalent to $10^{-3}.$ Hence, the equation above is equivalent to
\begin{array}{l}\require{cancel}
x=\log_{10} 10^{-3}
.\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}
x=-3\log_{10} 10
.\end{array}
Since $\log_b b=1,$ the equation above is equivalent to
\begin{array}{l}\require{cancel}
x=-3(1)
\\\\
x=-3
.\end{array}
