Answer
0.2994
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, $log_{6}\sqrt[3]5=\frac{log_{10}\sqrt[3]5}{log_{10}6}\approx\frac{0.2330}{0.7782}\approx0.2994$.
Recall that $b$ can be any positive number other than 1.