Answer
$\dfrac{1}{2}$
Work Step by Step
Using the properties of logarithms, the given expression, $
\log_{100} 10
,$ is equivalent to \begin{align*}
&
\log_{100} 10
\\&=
\log_{100} \sqrt{100}
\\&=
\log_{100} 100^{1/2}
\\\\&=
\dfrac{1}{2}\log_{100} 100
&(\text{use }\log_b x^y=y\log_bx)
\\\\&=
\dfrac{1}{2}(1)
&(\text{use }\log_b b=1)
\\\\&=
\dfrac{1}{2}
.\end{align*}Hence, $\log_{100} 10$ simplifies to $\dfrac{1}{2}$.
