Chapter 12 - Exponential Functions and Logarithmic Functions - 12.3 Logarithmic Functions - 12.3 Exercise Set - Page 803: 29

$-2$

Using $\log_bx^m=m\log_bx$ or the Power Rule of Logarithms, the given expression, $ \log_{10}0.01 ,$ is equivalent to \begin{array}{l}\require{cancel} \log_{10}\dfrac{1}{100} \\\\= \log_{10}\dfrac{1}{10^2} \\\\= \log_{10}(10)^{-2} \\\\= -2\log_{10}10 .\end{array} Since $\log_bb=1,$ the expression, $ \log_{10}10 ,$ simplifies to $1$. \begin{array}{l}\require{cancel} -2(1) \\\\= -2 .\end{array}