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: 27

Answer

$= \frac{1}{2}\log_{15} 3 + 2\log_{15} x + \frac{3}{2}\log_{15}y- 5\log_{15} z$

Work Step by Step

$= \log_{15} (\frac{\sqrt {3x^{4}y^{3}}}{z^{5}})$ $= \log_{15} \sqrt {3x^{4}y^{3}}- \log_{15} z^{5}$ $= \log_{15} (3x^{4}y^{3})^{\frac{1}{2}}- 5\log_{15} z$ $= \frac{1}{2}\log_{15} (3x^{4}y^{3})- 5\log_{15} z$ $= \frac{1}{2}\log_{15} 3 + \frac{1}{2}\log_{15} x^{4} + \frac{1}{2}\log_{15}y^{3}- 5\log_{15} z$ $= \frac{1}{2}\log_{15} 3 + \frac{4}{2}\log_{15} x + \frac{3}{2}\log_{15}y- 5\log_{15} z$ $= \frac{1}{2}\log_{15} 3 + 2\log_{15} x + \frac{3}{2}\log_{15}y- 5\log_{15} z$
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