Answer
$\log_{\frac{1}{2}}{\frac{1}{2}}=1$
Work Step by Step
Let
$x=\log_{\frac{1}{2}}{\frac{1}{2}}.$
RECALL:
$\log_{a}{y} = b \longleftrightarrow a^b = y.$
Use the definition above to convert the equation to an exponential equation and have
$(\frac{1}{2})^x=\frac{1}{2}.$
The bases are the same, so the exponents must be equal. Thus,
$x=1.$
Therefore $\log_{\frac{1}{2}}{\frac{1}{2}}=1$.