5. Solving Exponential Equations
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Use the calculator to graph two different functions, one for each side of the equation.
x ≈ -2.00 and x ≈ 4.33
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^(x-3)=x+2 ⇒ ly=4^(x-3) y=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 graphing, note that the second function is a linear function, so there can be even two intersections with the exponential function. Also, the exponent of 4 is x-3, so the function will be translated horizontally. To accommodate these issues, we should change the viewing window. Let's restrict the x-axis. -5 < x < 5 Also, we can change the scale of the x- and y-axis to increase by 2. We can do this by pushing WINDOW.
There are two points of intersection of these lines. To find those points we can use the intersect
option, which we get by pushing 2nd 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 ≈ -2.00 and x ≈ 4.33.