Answer
$\frac{1}{2}$
Work Step by Step
The definition of the logarithmic function says that $y=\log_a{x}$ if and only if $a^y=x$. Also, $a\gt0,a\ne1$ and $x\gt0$.
Hence $\log_{10} {\sqrt{10}}=y$, then $\left(10\right)^y=\sqrt{10}$ and we know that $\sqrt{10}=\left(10\right)^{\frac{1}{2}}.$
Thus, $\left(10\right)^{y}=\left(10\right)^{\frac{1}{2}}$. We know that $a^b=a^c\longrightarrow b=c$ if $a\ne1,a\ne-1$ (which applies here), hence $y=\frac{1}{2}$.
