18.4. Solving an Exponential Equation
We now return to the problem we started in the exploration of Sec. 18–2 but could not finish. We tried to solve the following equation for x.
- 24.0 = 2.48x
We will show several methods for solving this equation:
Using a calculator's equation solver
Using a symbolic algebra calculator
18.4.1. Graphical Solution
We can, of course, find an approximate graphical solution to this equation in the usual way.
Graphically solve 24.0 = 2.48x for x.
Solution: We move both terms to one side of the equals sign and set the resulting expression equal to y.
We graph this function, as shown, and find a root at x ≈ 3.50.
T1-83/84 screen for Example 46: y = 2.48x − 24.0. Tick marks on the horizontal axis are 1 unit apart.
18.4.2. Solution by Calculator
We can use any built-in equation solver to solve an exponential equation just as we used it earlier to solve other equations.
Solve the equation of Example 46 using the TI-83/84 equation solver.