Answer
$y=\log_{9}x$
Work Step by Step
We know the function takes the form:
$y=\log_{a}x$
We wish to find the base $a$. We use the point given: $(3,\frac{1}{2})$
$\frac{1}{2}=\log_{a}3$
$a^{\frac{1}{2}}=3$
$a=3^2=9$
Therefore the function is:
$y=\log_{9}x$