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

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

3

is

- x + 2,

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 < 3

Also, we can change the scale of the

y -

axis to increase by

5 .

We can do this by pushing

WINDOW .

There is one point of intersection of these curves. 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 $x \approx 1.78 .$

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