Chapter 12 - Exponential Functions and Logarithmic Functions - 12.3 Logarithmic Functions - 12.3 Exercise Set - Page 803: 19

$-1$

Using $\log_bx^m=m\log_bx$ or the Power Rule of Logarithms, the given expression, $ \log_{8}\dfrac{1}{8} ,$ is \begin{array}{l}\require{cancel} \log_{8}8^{-1} \\\\= -1\log_{8}8 \\\\= -\log_{8}8 .\end{array} Since the $\log_bb=1,$ the expression, $ -\log_{8}8 ,$ simplifies to \begin{array}{l}\require{cancel} -(1) \\\\= -1 .\end{array}