## Calculus 8th Edition

Published by Cengage

# Chapter 6 - Inverse Functions - 6.4* General Logarithmic and Exponential Functions - 6.4* Exercise: 15

#### Answer

The graphs of $y=\log_{b}x=\frac{logx}{logb}$, with various values of the base $b>1$ such as $b= 1.5,10,50$. Since, $\log_{b}1=0$ the graphs of all logarithmic functions pass through the point (0, 1). The graph is depicted as follows:

#### Work Step by Step

Since, change of base formula defines $\log_{a}x=\frac{logx}{loga}$ Therefore, $\log_{1.5}x=\frac{logx}{log1.5}$, $\log_{10}x=\frac{logx}{log10}$, $\log_{50}x=\frac{logx}{log50}$ 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 $b= 1.5,10,50$. 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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