Answer
$\dfrac{3}{2}$
Work Step by Step
Note that $8=2^3$.
Thus,
$\log_4{8}=\log_4{(2^3)}$
RECALL:
(1) $\log_a{b} = \dfrac{\log{b}}{log{a}}$
(2) $\log_a{(b^n)}=n \cdot \log_a{b}$
Use rule (1) above to obtain:
$\log_4{(2^3)} = \dfrac{\log{(2^3)}}{\log{4}}$
With $4=2^2$, the expression above is equivalent to:
$=\dfrac{\log{(2^3)}}{\log{(2^2)}}$
Use rule (2) above to obtain:
$\require{cancel}
\dfrac{\log{(2^3)}}{\log{(2^2)}}
\\=\dfrac{3\log{2}}{2\log{2}}
\\=\dfrac{3\cancel{\log{2}}}{2\cancel{\log{2}}}
\\=\dfrac{3}{2}$