Technical Mathematics, Sixth Edition

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 = 2.48^x

We will show several methods for solving this equation:

1. Graphical solution

2. Using a calculator's equation solver

3. Using a symbolic algebra calculator

4. Algebraically

18.4.1. Graphical Solution

We can, of course, find an approximate graphical solution to this equation in the usual way.

Example 46: 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. y = 2.48x − 24.0 We graph this function, as shown, and find a root at x ≈ 3.50.

T1-83/84 screen for Example 46: y = 2.48^x − 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.

Example 47: Solve the equation of Example 46 using the TI-83/84 equation solver. Solution: We select Solver from the menu and enter the equation (Screen 1). As for graphing, the equation must be in explicit form, with all terms on one side and 0 on the other side. Press . A new screen is displayed (Screen 2), showing a guess value ...