## College Algebra (11th Edition)

$x=-2$
$\bf{\text{Solution Outline:}}$ 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}