Technical Mathematics, Sixth Edition

18.5. Solving a Logarithmic Equation

18.5.1. Graphical Solution

▪ Exploration:

Try this. We have used our graphics calculators to find approximate solutions to many kinds of equations. Now use your calculator to graphically find the roots of the equation

3 log(x² + 2) = 6

In your exploration you probably graphed the function

y = 3 log(x² + 2) − 6

as shown, and found roots at x ≈ 9.90 and −9.90.

TI-83/84 graph of y = 3 log(x² + 2) − 6. Tick marks on the horizontal axis are 1 unit apart.

18.5.2. Using a Calculator's Equation Solver

We will now use a built-in equation solver to solve a logarithmic equation, just as we solved exponential equations earlier in this chapter.

TI-83/84 screen for Example 56. The computed value of x is shown, within the chosen bound.

Example 56: Solve the equation from the exploration using the TI-83/84 equation solver. Solution: We select Solver from the menu and enter the equation. Enter a new guess of x = 5 and a new bound of 0 to 20. Move the cursor to the line containing "x =" and press . The root falling within the selected bound is displayed. To find ...