Intermediate Algebra: Connecting Concepts through Application

Published by Brooks Cole
ISBN 10: 0-53449-636-9
ISBN 13: 978-0-53449-636-4

Chapter 6 - Logarithmic Functions - 6.4 Properties of Logarithms - 6.4 Exercises: 50

Answer

$= \ln \frac{35a^{4}b^{3}}{c^{3}}$

Work Step by Step

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