College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 4 - Exponential and Logarithmic Functions - Exercise Set 4.3: 35

Answer

$= \frac{2}{3}log_5(x)+\frac{1}{3}log_5(y) - \frac{2}{3}$

Work Step by Step

$= log_5(\sqrt[3] {\frac{x^{2}y}{25}})$ $= log_5(\frac{x^{2}y}{25})^{\frac{1}{3}}$ $= \frac{1}{3}log_5(\frac{x^{2}y}{25})$ $= \frac{1}{3}log_5(x^{2}y) - \frac{1}{3}log_5(25)$ $=\frac{1}{3}log_5(x^{2})+\frac{1}{3}log_5(y) - \frac{1}{3}log_5(5^{2})$ $= \frac{2}{3}log_5(x)+\frac{1}{3}log_5(y) - \frac{2}{3}log_5(5)$ $= \frac{2}{3}log_5(x)+\frac{1}{3}log_5(y) - \frac{2}{3}$
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