College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 4 - Exponential and Logarithmic Functions - Exercise Set 4.3 - Page 477: 89


False; $ln(e)=1$

Work Step by Step

We are given that $ln(e)=0$. We know that $ln(x)$ is a natural logarithm with an understood base of $e$. Therefore, $ln(e)=log_{e}e$. Based on the definition of the logarithmic function, we know that $y=log_{b}x$ is equivalent to $b^{y}=x$ (for $x\gt0$ and $b\gt0$, $b\ne1$). Therefore, $log_{e}e=ln(e)=1$, because $e^{1}=e$. The given statement is false.
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