Chapter 3.2, Problem 36E

To determine

To plot: the functions $f\left(x\right)={10}^x$ and $g\left(x\right)=\log x$ on the same coordinates.

Explanation of Solution

Given:

The functions are $f\left(x\right)={10}^x$ and $g\left(x\right)=\log x$ .

Calculation:

Consider $y={10}^x$ and $y=\log x$ ,

Take some of values of x and find the values of y in first equation as follows:

x	y
0	1
-2	0.01
0.2	1.585
0.1	1.259
0.3	1.996
0.5	3.162

Draw above coordinates and join them to make plot of $y={10}^x$ as shown below:

  

Now, consider second equation $y=\log x$ and simplify as follows:

  $x={10}^y$

From above equation, it is clear that both the functions have opposite axis means y replaces x and x replaces y.

Thus, the coordinates are just same by changing coordinates x and y as given below:

y	x
0	1
-2	0.01
0.2	1.585
0.1	1.259
0.3	1.996
0.5	3.162

Draw above coordinates and join them to make plot of $x={10}^y\text{}\text{or}y=\log x$ as shown below:

  

Take both the plots on the same plane as shown below: