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: 56

Answer

$\ln{[(x-4)^{\frac{1}{2}}(x^2+4x)^{\frac{5}{2}}]}$

Work Step by Step

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