Answer
.125
Work Step by Step
We are given $log_{b}3=.5$ and $log_{b}5=.7$.
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, $log_{b}\sqrt[4] 3=log_{b}3^{\frac{1}{4}}=\frac{1}{4}log_{b}3=\frac{1}{4}\times.5=.125$.