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: 14

Answer

The graphs of $y=\log_{b}x=\frac{logx}{logb}$, with various values of the base $b>1$ such as $b= 2,4,6,8$. Since, $\log_{b}1=0$ the graphs of all logarithmic functions pass through the point (0, 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, $\log_{2}x=\frac{logx}{log2}$, $\log_{4}x=\frac{logx}{log4}$, $\log_{6}x=\frac{logx}{log6}$ and $\log_{8}x=\frac{logx} {log8}$ The graphs of $y=\log_{b}x=\frac{logx}{logb}$, with various values of the base $b>1$ such as $b= 2,4,6,8$. Since, $\log_{b}1=0$ the graphs of all logarithmic functions pass through the point (0, 1). The graph is depicted as follows:
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