Answer
.2386
Work Step by Step
We are given that $log_{10}2=.3010$ and $log_{10}9=.9542$.
We know that $log_{b}x^{r}=rlog_{b}x$ (where $x$ and $b$ are positive real numbers, $b\ne1$, and $r$ is a real number).
Therefore, $log_{10}\sqrt[4] 9=\frac{1}{4}log_{10}9=\frac{1}{4}(.9542)=.2386$.