#### Answer

$\log_4{2}=\frac{1}{2}$

#### Work Step by Step

Let
$x=\log_4{2}.$
RECALL:
$\log_{a}{y} = b \longleftrightarrow a^b = y.$
Use the definition above to convert the equation to an exponential equation and have
$4^x=2.$
Write each side in base 2 to have
$(2^2)^x=2
\\2^{2x}=2$
The bases are the same, so the exponents must be equal. Thus,
$2x=1
\\x = \frac{1}{2}.$
Therefore $\log_4{2}=\frac{1}{2}.$