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 4.2: 92



Work Step by Step

We know that the logarithmic function of base $e$, or the natural logarithmic function, can be written as $f(x)=ln(x)$ or as $f(x)=log_{e}x$. Therefore, $ln(\frac{1}{e^{7}})=log_{e}\frac{1}{e^{7}}$. From the definition of the logarithmic function on page 456, we know that $b^{y}=x$ is equivalent to $y=log_{b}x$ (for $x\gt0$, $b\gt0$, and $b\ne1$). Therefore, $log_{e}\frac{1}{e^{7}}=-7$, because $e^{-7}=\frac{1}{e^{7}}$.
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