Answer
$x=-1$
Work Step by Step
Recall the definition of a logarithm (pg. 451):
$\log_{b}{x}=y$ iff $b^y=x$
Applying this definition to our equation (with $b=2, y=1/2, x=x$), we get:
$\log_{2}{\frac{1}{2}}=x$
$\log_{2}2^{-1}=x$
Next, recall the power property of logarithms (pg. 462):
$\log_b{m^n}=n\log_b{m}$
Applying this property, we get:
$-1\log_{2}2=x$
$-1\cdot1=x$ (because $2^1=2$)
$x=-1$
We confirm that the answer works:
$2^{-1}=1/2$
$\frac{1}{2}=\frac{1}{2}$
