Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 5 - 5.3 - Properties of Logarithms - 5.3 Exercises - Page 387: 96


True. The proof is given below.

Work Step by Step

Make $x=\frac{a}{b}$ and use the One-to-One Property: $\ln x=\ln\frac{a}{b}=ln a-\ln b$ If $f(x)\lt0$, then $ln a- \ln b\lt0~→~\ln a\lt\ln b$ We know that $f(x)=\ln x$ is ascending for all $x$ in the Domain: $(0,∞)$. So, if $\ln a\lt\ln b$ then $a\lt b~→~\frac{a}{b}\lt1$, that is, $x\lt1$.
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