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: 35

Answer

$\log_5{3} + 2\log_5{x}-3\log_5{y}$

Work Step by Step

RECALL: (1) $\log_b{(PQ)} = \log_b{P} + \log_b{Q}$ (2) $\log_b{(\frac{P}{Q})} = \log_b{P} - \log_b{Q}$ (3) $\log_b{(x^n)}=n(\log_b{x})$ Use rule (2) above to obtain: $=\log_5{(3x^2)} - \log_5{(y^3)}$ Use rule (1) above to obtain: $=\log_5{3} + \log_5{(x^2)} -\log_5{(y^3)}$ Use rule (3) above to obtain: $=\log_5{3} + 2\log_5{x}-3\log_5{y}$
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