Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 5 - 5.3 - Properties of Logarithms - 5.3 Exercises - Page 385: 58


$\log_2x^4\sqrt {\frac{y}{z^3}}=4\log_2x+\frac{\log_2y}{2}-\frac{3\log_2z}{2}$

Work Step by Step

$\log_2x^4\sqrt {\frac{y}{z^3}}=\log_2x^4+\log_2(\frac{y}{z^3})^\frac{1}{2}=4\log_2x+\frac{1}{2}\log_2\frac{y}{z^3}=4\log_2x+\frac{1}{2}(\log_2y-\log_2z^3)=4\log_2x+\frac{1}{2}(\log_2y-3\log_2z)=4\log_2x+\frac{\log_2y}{2}-\frac{3\log_2z}{2}$
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