Functions Modeling Change: A Preparation for Calculus, 5th Edition

Published by Wiley
ISBN 10: 1118583191
ISBN 13: 978-1-11858-319-7

Chapter 5 - Logarithmic Functions - Exercises to Skills for Chapter 5 - Page 232: 35



Work Step by Step

First, use the fact that $\log a^b= b \log a$ to simplify the expression to $$2 \ln x^{-2} + \ln x^4$$ $$\ln (x^{-2})^2+\ln x^4$$ Since $(a^m)^n=a^{mn}$, $$=\ln (x^{-4})+\ln(x^4)$$ Finally, using the fact that $\ln(a)+\ln(b)=\ln(ab)$ the expression simplifies to $\ln(x^{-4}(x^4))=\ln(x^4/x^4)=\ln(1)=\ln e^0=0$
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