To solve the equation by graphing, we first have to create two functions. Each side of the given equation will become its own equation.

4^{7 x} = 250 \Rightarrow y = 4^{7 x} y = 250

Now we want to draw these graphs using a calculator. We can do this by pressing the

Y =

button and typing the equations in the two first rows.

Before we graph these functions, notice that the second function is a horizontal line at

y = 250,

so we will not be able to see this in the standard viewing window. Also, the exponent of

4

is

7 x,

so the function will grow very quickly. In order to accommodate these issues, we should change the viewing window. Let's restrict the

x -

axis.

- 1 < x < 1

We can change the scale of the

y -

axis to increase by

50 .

We can do this by pushing

WINDOW .

There is one point of intersection of these graphs. To find this point we can use the intersect option, which we get by pushing $2 nd$ and $TRACE .$ Now, we select both graphs and provide the calculator with a guess as to where the intersection might be.

The solution to the equation is $x \approx 0.5690 .$

Exercise

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