Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 6 - Inverse Functions - 6.4* General Logarithmic and Exponential Functions - 6.4* Exercise - Page 463: 16

Answer

The function $lnx$ and $y=\log_{10}x$ are inverse functions of $10^{x}$ and $e^{x}$, respectively.From the graph, we can conclude that the functions lnx and $y=\log 10(x)$ intersect at point $x = 1$ and their inverse functions intersect at $y = 1$. The graph is depicted as follows:
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Work Step by Step

Since, change of base formula defines $\log_{a}x=\frac{logx}{loga}$ Therefore, $y=lnx$, $y=\log_{10}x=\frac{logx}{log10}$, $y=e^{x}$ and $y=10^{x}$ The most important logarithmic functions have base $b>1$ The fact that $y=b^{x}$ is a very rapidly increasing function for $x>0$ is reflected in the fact that $y=\log_{b}x$ is a very slowly increasing function for $x>1$ . The function $lnx$ and $y=\log_{10}x$ are inverse functions of $10^{x}$ and $e^{x}$, respectively.From the graph, we can conclude that the functions lnx and $y=\log 10(x)$ intersect at point $x = 1$ and their inverse functions intersect at $y = 1$. The graph is depicted as follows:
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