Answer
$\frac{1}{2}log_{b}3-\frac{1}{2}log_{b}y$
Work Step by Step
We know that $log_{b}\frac{x}{y}=log_{b}x-log_{b}y$ (where $x$, $y$, and $b$ are positive real numbers and $b\ne1$).
Therefore, $log_{b}\sqrt \frac{3}{y}=log_{b}\frac{3^{\frac{1}{2}}}{y^{\frac{1}{2}}}=log_{b}3^{\frac{1}{2}}-log_{b}y^{\frac{1}{2}}$.
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, $log_{b}3^{\frac{1}{2}}-log_{b}y^{\frac{1}{2}}=\frac{1}{2}log_{b}3-\frac{1}{2}log_{b}y$.