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 - Page 425: 52



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