Answer
$\log_4{8}=\frac{3}{2}$
Work Step by Step
Let
$x=\log_4{8}.$
RECALL:
$\log_{a}{y} = b \longleftrightarrow a^b = y.$
Use the definition above to convert the equation to an exponential equation and have
$4^x=8.$
Write each side in base 2 to have
$(2^2)^x=2^3
\\2^{2x}=2^3.$
The bases are the same, so the exponents must be equal. Thus,
$2x=3
\\x = \frac{3}{2}.$
Therefore $\log_4{8}=\frac{3}{2}$.