Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 9 - Section 9.4 - Properties of Logarithms - Exercise Set - Page 713: 92


a) $\dfrac{1}{2}$ b) $\log_{36}[\dfrac{x(x^2-4)^5}{6(x+2)}]$

Work Step by Step

a) Since, $\log_{36} {6}=\log _{36}(36)^{1/2}=\dfrac{1}{2}$ b) From part (a), we have $\log_{36} x+5\log_{36}(x^2-4)-\log_{36}(x+2)-\dfrac{1}{2}=\log_{36} x+5\log_{36}(x^2-4)-\log_{36}(x+2)-\log_{36} {6}$ or, $\log_{36} x+5\log_{36}(x^2-4)-\log_{36}(x+2)-\dfrac{1}{2}=\log_{36} x+\log_{36}(x^2-4)^5-[\log_{36}(x+2)+\log_{36}6]$ or, $\log_{36} x+5\log_{36}(x^2-4)-\log_{36}(x+2)-\dfrac{1}{2}=\log_{36} [x(x^2-4)^5]-\log_{36} [6(x+2)]$ or, $\log_{36} x+5\log_{36}(x^2-4)-\log_{36}(x+2)-\dfrac{1}{2}=\log_{36}[\dfrac{x(x^2-4)^5}{6(x+2)}]$ Hence, a) $\dfrac{1}{2}$ b) $\log_{36}[\dfrac{x(x^2-4)^5}{6(x+2)}]$
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