1. Chapter 4 4-5 Exponential and logarithmic equations

2. Objectives Solve exponential and logarithmic equations and inequalities. Solve problems involving exponential and logarithmic equations.

3. Exponential equation O An exponential equation is an equation containing one or more expressions that have a variable as an exponent. O To solve exponential equations: Try writing them so that the bases are all the same. Take the logarithm of both sides.

4. Example#1 O Solve for x O 9 8 – x = 27 x – 3

5. Example#2 O Solve for x O 4 x – 1 = 5

6. Example#3 O Solve O 2 3x = 15

7. Student guided practice O Do problems 2 -5 in your book page 270

8. Biology Application O Suppose a bacteria culture doubles in size every hour. How many hours will it take for the number of bacteria to exceed 1,000,000?

9. Logarithmic equation O A logarithmic equation is an equation with a logarithmic expression that contains a variable. You can solve logarithmic equations by using the properties of logarithms.

10. Example#4 O Solve O log 6 (2x – 1) = –1

11. Example#5 O Solve O log 4 100 – log 4 (x + 1) = 1

12. Example#6 O Solve O log 5 x 4 = 8

13. Student guided practice O Do problems 9 -13 in your book page 270

14. Example#7 O Use a table and graph to solve O 2 x + 1 > 8192x.

15. Example#8 O Using a table and graph solve O log(x + 70) = 2log ( x/3 )

16. Example#9 Use a table and graph to solve 2 x > 4 x – 1.

17. Student guided practice O Do problems 17-19 in your book page 270

18. Homework O Do even problems from 21-36 in your book page 270

19. Closure Today we saw how to solve exponential and logarithmic functions. Next class we are going to continue with the natural base, e.