College Algebra 7th Edition

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

Chapter 4, Exponential and Logarithmic Functions - Chapter 4 Review - Concept Check: 48

Answer

$\log{4} +3\log{x}-3\log{y}-5\log{(x-1)}$

Work Step by Step

RECALL: (1) $\log_a{(P^n)}=n \cdot \log_a{P}$ (2) $\log_a{(PQ)}=\log_a{P} + \log_a{Q}$ (3) $\log_a{(\frac{P}{Q})} = \log_a{P} - \ln{Q}$ Use rule (3) above to obtain: $=\log{(4x^3)-\log{[(y^3(x-1)^5)}}]$ Use rule (2) above to obtain: $=[\log{4} + \log{(x^3)}]-[\log{(y^3)}+\log{(x-1)^5}] \\=\log{4} +\log{(x^3)}-\log{(y^3)}-\log{(x-1)^5}$ Use rule (1) above to obtain: $=\log{4} +3\log{x}-3\log{y}-5\log{(x-1)}$
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