College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 6 - Section 6.5 - Properties of Logarithms - 6.5 Assess Your Understanding: 52

Answer

$3\log x+\dfrac {1}{2}\log \left( x+1\right) -2\log \left( x-2\right) $

Work Step by Step

We use the rules of logarithms to obtain: $\log \dfrac {x^3\sqrt {x+1}}{\left( x-2\right) ^{2}}=\log \left( x^3\times \sqrt {x+1}\right) -\log \left( x-2\right) ^{2}=\log x^{3}+\log \left( x+1\right) ^{\dfrac {1}{2}}-2\log \left( x-2\right) =3\log x+\dfrac {1}{2}\log \left( x+1\right) -2\log \left( x-2\right) $
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