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

ln 2 x = e^{x - 3} \Rightarrow y = ln 2 x y = e^{x - 3}

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 exponent of

e

is

x - 3,

so the function will be translated horizontally and we will not be able to see it in the standard viewing window. In order to accommodate this issue, we should change the viewing window. Let's restrict the

x -

axis.

- 1 < x < 5

Let's now graph the functions.

There are two points of intersection of these curves. To find those points we can use the intersect option, which we get by pushing $2 nd$ and $TRACE .$

After selecting the "intersect" option, we need to choose left and right boundaries for one of the points. Finally, the calculator asks for a guess where the intersection point might be. After that, it will calculate the exact point for us. We will have to do this twice, once for each point.

The solutions to the equation are $x \approx 0.54$ and $x \approx 3.69 .$

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