Chapter 1, Problem 30RE

To determine

To find: The graph for the given equations on the same screen for the two or three values of $a>1$ . Also, find the function that has the largest values and smallest value for the for $x$ .

Answer to Problem 30RE

The graph for the given functions is shown in Figure 1, Figure 2 and Figure 3 and the largest value is of the function $y=a^x$ and the function has the smallest value for large value of $x$ .

Explanation of Solution

Given:

The given function are,

  $\begin{array}{l}y=a^x\\ y=x^a\\ y={\log }_{a}x\end{array}$

Calculation:

Consider the given functions,

  $\begin{array}{l}y=a^x\\ y=x^a\\ y={\log }_{a}x\end{array}$

Consider the case when $a=2$ .

The graph for all the function is shown in Figure 1

  

Figure 1

Consider the case when $a=6$ .

The graph for all the function is shown in Figure 2

  

Figure 2

Consider the case when $a=10$ .

The graph for all the function is shown in Figure 3

  

Figure 3

From the graph in Figure 1, 2, and 3 it is observed that the function $y=a^x$ has the largest values and $y={\log }_{a}x$ has the smallest value for the larger values of $x$ .