Chapter 3.4, Problem 157E

a.

To determine

To use : the graphing utility to graph the two functions

Explanation of Solution

Given information : The question is

Let $f\left(x\right)={\log }_{a}x\&g\left(x\right)=a^x$ here $a=1.2$

Graph : Sketch the graph using graphing utility.

Step 1: Press WINDOW button to access the Window editor.

Step 2: Press $\boxed{\text{Y=}}$ button.

Step 3: Enter the expression ${\log }_{a}x\&a^x$ which is required to graph.

Step 4: Press $\boxed{\text{GRAPH}}$ button to graph the function.

The graph is obtained as:

  

Interpretation :

From the above graph the red line shows the function $f\left(x\right)={\log }_{a}x$ and the blue line shows the function $g\left(x\right)=a^x$

b.

To determine

To calculate : the point of intersection from part (a) from one point

Answer to Problem 157E

The points of intersection are $\left(1.258,1.258\right)\&\left(14.767,14,767\right)$

Explanation of Solution

Given information : The question is

Let $f\left(x\right)={\log }_{a}x\&g\left(x\right)=a^x$

Calculation :

From the graph shows in part (a) the points of intersection are $\left(1.258,1.258\right)\&\left(14.767,14,767\right)$

Exploring the values of $a$ using a graphing utility the two graphs have one point of intersection when $a\approx 1.445$

c.

To determine

To calculate : the point of intersection from part (b) from two point

Answer to Problem 157E

The points of intersection are $\left(1.258,1.258\right)\&\left(14.767,14,767\right)$

Explanation of Solution

Given information : The question is

Let $f\left(x\right)={\log }_{a}x\&g\left(x\right)=a^x$

Calculation :

From the graph shows in part (a) the points of intersection are $\left(1.258,1.258\right)\&\left(14.767,14,767\right)$

Exploring the values of $a$ using a graphing utility the two graphs have two point of intersection when $1<a<1.445$