Answer
$-1.161$
Work Step by Step
Using the properties of logarithms, the given expression, $
\log_b \dfrac{1}{5}
,$ is equivalent to
\begin{array}{l}\require{cancel}
\log_b 1-\log_b 5
.\end{array}
Since it is given that $\log_b 5=1.161 $ and that the logarithm of $1$ to any defined base is $0$, the expression above, $
\log_b 1-\log_b 5
$, evaluates to
\begin{array}{l}\require{cancel}
0-1.161
\\\\=
-1.161
.\end{array}
