Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 9 - Section 9.5 - Common and Natural Logarithms - 9.5 Exercises: 23

Answer

-11.4007

Work Step by Step

We know that logarithms with base $e$ are natural logarithms, and $ln(x)$ can be written as $log_{e}x$. Therefore, $ln(e^{-11.4007})=log_{e}e^{-11.4007}$. We know that for all positive numbers $a$ (where $a\ne1$), and all positive numbers $x$, $y=log_{a}x$ means the same as $x=a^{y}$. Therefore, $log_{e}e^{-11.4007}=-11.4007$, because $e^{-11.4007}=e^{-11.4007}$.
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