Answer
$\log{4} +3\log{x}-3\log{y}-5\log{(x-1)}$
Work Step by Step
RECALL:
(1) $\log_a{(P^n)}=n \cdot \log_a{P}$
(2) $\log_a{(PQ)}=\log_a{P} + \log_a{Q}$
(3) $\log_a{(\frac{P}{Q})} = \log_a{P} - \ln{Q}$
Use rule (3) above to obtain:
$=\log{(4x^3)-\log{[(y^3(x-1)^5)}}]$
Use rule (2) above to obtain:
$=[\log{4} + \log{(x^3)}]-[\log{(y^3)}+\log{(x-1)^5}]
\\=\log{4} +\log{(x^3)}-\log{(y^3)}-\log{(x-1)^5}$
Use rule (1) above to obtain:
$=\log{4} +3\log{x}-3\log{y}-5\log{(x-1)}$
