Answer
$\log{(x^3y^4)}$
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) $\log_a{(\frac{P}{Q})}= \log_a{P} - \log_a{Q}$
(4) $a^m \cdot a^m=a^{m+n}$
Use rule (1) above to obtain
$\log{x}+\log{(x^2y)} +3\log{y}
\\= \log{x}+\log{(x^2y)} +\log{(y^3)}$
Use rule (2) above to obtain:
$\log{x}+\log{(x^2y)} +\log{(y^3)}
\\= \log{[x(x^2y)(y^3)]} $
Use rule (4) above to obtain:
$\log{[x(x^2y)(y^3)]} =\log{(x^{1+2}y^{1+3})}=\log{(x^3y^4)}$