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: 52

Answer

$\ln{\left(\frac{8x^2}{(x+4)^{\frac{1}{2}}}\right)}$

Work Step by Step

RECALL: (1) $\ln{P} + \ln{Q} = \ln{(PQ)}$ (2) $\ln{P} - \ln{Q} = \ln{(\frac{P}{Q})}$ (3) $a(\ln{x}) = \ln{(x^a)}$ Use rule (3) above to obtain: $=\ln{(2^3)}+\ln{(x^2)}-\ln{[(x+4)^{\frac{1}{2}}]} \\=\ln{8}+\ln{(x^2)}-\ln{[(x+4)^{\frac{1}{2}}]}$ Use rule (1) above to obtain: $=\ln{(8x^2)}-\ln{[(x+4)^{\frac{1}{2}}]}$ Use rule (2) above to obtain: $=\ln{\left(\frac{8x^2}{(x+4)^{\frac{1}{2}}}\right)}$
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