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: 36

Answer

$= \frac{1}{5}log_2(x) + \frac{4}{5}log_2(y) - \frac{4}{5}$

Work Step by Step

$= log_2(\sqrt[5] {\frac{xy^{4}}{16}})$ $=log_2(\frac{xy^{4}}{16})^{\frac{1}{5}}$ $=\frac{1}{5}log_2(\frac{xy^{4}}{16})$ $= \frac{1}{5}log_2(xy^{4}) - \frac{1}{5}log_2(16)$ $=\frac{1}{5}log_2(x) + \frac{1}{5}log_2(y^{4}) - \frac{1}{5}log_2(2^{4})$ $= \frac{1}{5}log_2(x) + \frac{4}{5}log_2(y) - \frac{4}{5}log_2(2)$ $= \frac{1}{5}log_2(x) + \frac{4}{5}log_2(y) - \frac{4}{5}$
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