Answer
$\dfrac{1}{2}$
Work Step by Step
Note that $y=\log_a x \text{ is equivalent to } x= a^y$
Thus, if $y = \log_{10} \sqrt{10},$ then $10^y=\sqrt{10}$
Since $\sqrt{10}=10^{\frac{1}{2}},$ then
$10^y=10^{\frac{1}{2}}$
Use the rule $a^m=a^n \implies m=n$ to obtain:
$y=\dfrac{1}{2}$
Therefore,
$ \log_{10} \sqrt{10} = \boxed{\dfrac{1}{2}}$
