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