Answer
$y=\log_{2}x$
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: $(\frac{1}{2},-1)$
$-1=\log_{a}\frac{1}{2}$
$a^{-1}=\frac{1}{2}$
$a=2$
Therefore the function is:
$y=\log_{2}x$