Answer
$3\log_2{z}$
Work Step by Step
RECALL:
(1) $\log_a{(MN)} = \log_a{M} + \log_a{N}$
(2) $\log_a{\left(\dfrac{M}{N}\right)} = \log_a{M} - \log_a{N}$
(3) $\log_a{a} = 1$
Note that $z^3=z(z)(z)$. So the given expression is equivalent to:
$=\log_2{\left(z\cdot z\cdot z\right)}$
Using rule (1) above gives:
$=\log_2{z} + \log_2{z} + \log_2{z}$
Factor out $\log_2{z}$ to obtain:
$=\log_2{z}(1+1+1)
\\=\log_2{z}(3)
\\=3\log_2{z}$
