Answer
$= \ln \frac{35a^{4}b^{3}}{c^{3}}$
Work Step by Step
$\frac{1}{2} \ln 7 + \frac{1}{2}\ln 5a + \frac{3}{2} \ln ab - 3 \ln c$
$= \ln \sqrt 7 + \ln \sqrt {5a} + \ln \sqrt {(ab)^{3}} - \ln c^{3}$
$= \ln \sqrt 7 + \ln \sqrt {5a} + \ln \sqrt {a^{3}b^{3}} - \ln c^{3}$
$= \ln \sqrt {7(5a)(a^{3}b^{3})}- \ln c^{3}$
$= \ln 35a^{4}b^{3}- \ln c^{3}$
$= \ln \frac{35a^{4}b^{3}}{c^{3}}$
