Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 7 - Exponential Functions - 7.3 Logarithms and Their Derivatives - Preliminary Questions - Page 342: 2



Work Step by Step

Let $\ln x>0$, then we have $$\ln x=-a, \quad a>0.$$ Hence, $$ x=e^{-a}=\dfrac{1}{e^a}$$ Note that the lowest value that $x$ can take on is near $e^{\infty}\approx 0$, excluding zero itself. The largest value is $e^0=1$, excluding $1$ itself (because $a\gt 0$). So, $\ln x $ is negative for $(0,1)$.
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