Answer
$\frac{1}{2}$
Work Step by Step
Based on the definition of the common logarithm, we know that $log(x)=log_{10}x$.
Furthermore, recall that $log_{b}x=y$ is equivalent to the statement $b^{y}=x$ (where $x\gt0$, $y$ is a real number, and $b\gt0$ and $b\ne1$).
Therefore, $log(\sqrt 10)=log_{10}\sqrt 10=\frac{1}{2}$, because $10^{\frac{1}{2}}=\sqrt 10$.