#### Answer

0.3155

#### Work Step by Step

If $a\gt0$, $a\ne1$, $b\ne1$, and $x\gt0$, then we know that $log_{a}x=\frac{log_{b}x}{log_{b}a}$.
Therefore, $log_{3}\sqrt2=\frac{log_{10}\sqrt2}{log_{10}3}\approx\frac{0.1505}{0.4771}\approx0.3155$.
Recall that $b$ can be any positive number other than 1.