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: 36

Answer

$5\log_2{s} -\log_2{7}-2\log_2{t}$

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: $=\log_2{(s^5)} - \log_2{(7t^2)}$ Use rule (1) above to obtain: $=\log_2{(s^5)} - (\log_2{7} +\log_2{(t^2)}$ Use rule (3) above to obtain: $=5\log_2{s} -(\log_2{7}+2\log_2{t})$ Subtract each term of the binomial to obtain: $=5\log_2{s} -\log_2{7}-2\log_2{t}$
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