1. Solving Exponential and Logarithmic Equations Section 8.6

2. WHAT YOU WILL LEARN: 1.How to solve equations that have either a logarithmic or exponential “expression”.

3. Solving Exponential Equations In order for two exponential expressions to be equal, both the bases and the exponents must be equal. 4 x = 4 x 4 3 = 4 x What does x have to equal?

4. Example Solve 4 3x = 8 x+1

5. You Try Solve 2 4x = 32 x-1

6. Another Way to Solve Taking a Logarithm of Each Side Solve 2 x = 7

7. You Try Solve 4 x = 15

8. Example 3 Taking a Logarithm of each Side – Multiple Steps. Solve: 10 2x-3 + 4 = 21

9. You Try Solve 5 x+2 + 3 = 25

10. Example 4 Solving Logarithmic Equations Solve log 3 (5x – 1) = log 3 (x + 7)

11. You Try Solve log 4 (x+3) = log 4 (8x+17)

12. Solving Equations with a Mix of Logs and Numbers Example – Solve: log 5 (3x + 1) = 2

13. You Try Solve log 4 (x + 3) = 2

14. Checking for Extraneous Solutions You can get extraneous solutions when solving these equations. You need to check your answers! Solve: log 5x + log (x – 1) = 2

15. You Try Solve log 6 (x + 5) + log 6 x = 2

16. Homework page 505, 22-24 even, 25, 29, 31, 32, 37, 38, 43-53 odd, 63, 65