Write the equation as two functions and then use a graphing calculator.
x=1, x=3 Can It Be Solved Algebraically? No
Practice makes perfect
To solve this equation graphically, we will treat each side as a separate function.
3x-1= 2^x
⇓
f(x)= 3x-1 and g(x)= 2^x
Graphing the Functions
To find the function's point(s) of intersection we will graph the functions. The x-values of the points will be the solutions to the original equation. Pull out your graphing calculator, push Y= and write the functions on the first two rows.
By pushing GRAPH the calculator will draw the functions in a coordinate plane.
Finding the Intersections
To find the points of intersection, push 2nd and then TRACE. This opens a menu where we choose the option intersect.
Having picked intersect, choose the first and second curve, and pick a best guess for the first point of intersection. After accepting the three questions, the coordinates of the intersection will be shown.
Since we're only interested in the x-values, the solution to the equation is x=1. To find the second solution, we repeat the procedure, but this time placing the cursor closer to the second point of intersection.
The second solution is x=3.
Can It Be Solved Algebraically?
When solving an equation with one variable we want to isolate that variable on one side of the equation. However, here we have x as an exponent on the left-hand side. To isolate it we must get it down from the exponent. Currently we do not have the knowledge to do this. Therefore, we cannot solve the equation algebraically.
