College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 4, Exponential and Logarithmic Functions - Section 4.4 - Laws of Logarithms - 4.4 Exercises: 32

Answer

$\log_3{x} + \frac{1}{2}\log_3{y}$

Work Step by Step

RECALL: (1) $\log_b{(PQ)} = \log_b{P} + \log_b{Q}$ (2) $\sqrt{a} = a^{\frac{1}{2}}$ (3) $\log_b{a^x} = x \cdot \log_b{a}$ Use rule (1) above to obtain: $=\log_3{x} + \log_3{\sqrt{y}}$ Use rule (2) above to obtain: $=\log_3{x} + \log_3{y^{\frac{1}{2}}}$ Use rule (3) above to obtain: $=\log_3{x} + \frac{1}{2}\log_3{y}$
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