#### Answer

0.6826

#### 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, $log_{5}3=\frac{log_{10}3}{log_{10}5}\approx\frac{0.4771}{0.6990}\approx0.6826$.
Recall that $b$ can be any positive number other than 1.