Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 4 - Review - Exercises - Page 389: 56


$$\ln \sqrt {(x-4)(x^2+4x)^5}$$

Work Step by Step

$Combine$ $into$ $a$ $single$ $logarithm:$ $\frac{1}{2}[\ln (x-4) + 5\ln (x^2+4x)]$ Use the Third Law of Logarithms $\frac{1}{2}[\ln (x-4) + 5\ln (x^2+4x)]$ = $[\ln (x-4) + 5\ln (x^2+4x)]^{\frac{1}{2}}$ Use the Third Law of Logarithms for $5\ln (x^2+4x)$ $5\ln (x^2+4x)$ = $\ln (x^2+4x)^5$ $[\ln (x-4) + \ln (x^2+4x)^5]^{\frac{1}{2}}$ Use the First Law of Logarithms inside the brackets $\ln (x-4) + \ln (x^2+4x)^5$ = $\ln ((x-4)(x^2+4x)^5)$ $\ln ((x-4)(x^2+4x)^5)^{\frac{1}{2}}$ Simplify $$\ln \sqrt {(x-4)(x^2+4x)^5}$$
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