Answer
$-1$
Work Step by Step
Using $\log_bx^m=m\log_bx$ or the Power Rule of Logarithms, the given expression, $
\log_{10}0.1
,$ is equivalent to
\begin{array}{l}\require{cancel}
\log_{10}\dfrac{1}{10}
\\\\=
\log_{10}(10)^{-1}
\\\\=
-1\log_{10}10
.\end{array}
Since $\log_bb=1,$ the expression, $
\log_{10}10
,$ simplifies to $1$.
\begin{array}{l}\require{cancel}
-1(1)
\\\\=
-1
.\end{array}