Answer
$2\log_b{x}+\log_b{y}-2\log_b{z}$
Work Step by Step
RECALL:
(1) $\log{(b^c)}=c \cdot \log{b}$
(2) $\log_b{(xy)} = \log_b{x} + \log_b{y}$
(3) $\log_b{(\frac{x}{y})}=\log_b{x} - \log_b{y}$
Use rule (3) above to obtain:
$=\log_b{(x^3y)}-\log_b{(z^2)}$
Use rule (2) above to obtain:
$=\log_b{(x^2)} +\log_b{y} - \log_b{(z^2)}$
Use rule (1) above to obtain:
$=2\log_b{x}+\log_b{y}-2\log_b{z}$
