Solving Exponential Equations

1
Solving Exponential Equations
2
One-to-One Properties
3
Inverse Properties
4
General strategies for solving exponential
equations

1. Isolate the exponential expression.
2. Use the one-to-one property.

5
Example 1 Solve 4e2x 16

• Isolate the exponential expression.
• Take the natural log of both sides.
• Apply the inverse property.
• Solve for x.

6
Example 2 Solve 5ex2 8 14

• Isolate the exponential expression.
• Take the natural log of both sides.
• Apply the inverse property.
• Solve for x.

7
Try This

• Solve ex-2 7 59

8
Example 3 Solve 3x 1 5

• Isolate the exponential expression.
• Take the log of both sides.
• Apply the power property.
• Solve for x.

9
Example 4 Solve e2x ex 20 0

• Replace ex with u to help us factor.
• Apply the Zero Product Property.

10
Example 4 Solve e2x ex 20 0
Continued

• Solve for x.

ex cant be negative
11
Try This

• Solve e2x 3ex 2 0

12
Class Practice

• 4e2x 5
• 72x 1/49
• 32x-1 27
• 8(10)3x 12
• 23-x 565