1. Solving Exponential and Logarithmic Functions
Section 3.4

2. Solve exponential and logarithmic equations.
Objective
Solve exponential and logarithmic equations.

3. Relevance
Learn how to evaluate data from real world applications that fit into an exponential or logarithmic model.

4. 2 Basic Strategies for Solving Exponential & Log Equations
One-To-One Properties
Inverse Properties

5. Practice: Solve the equations and determine the property used.

6. Solve

7. Solve

8. Solve

9. Solve

10. Solve

11. Solve

12. Solve

13. Solve

14. Properties of Logarithms
Section 3.3

15. Properties of Logarithms

16. Simplify: (Condense)

17. Condense:

18. Condense:

19. Condense:

20. Condense:

21. Condense:

22. Condense:

23. Condense:

24. Condense:

25. Condense and Evaluate if Possible:

26. Expand:

27. Expand:

28. Expand:

29. Expand:

30. Solve Logarithms
Section 3.3

31. Solve:

32. Solve:

33. Extraneous Solutions
Domain Restrictions!

34. Solve:

35. Solve:

36. Solve:

37. Solve By Substitution
Section 3.3

38. What Do You Think?

39. Solve by Using Substitution

40. Solve by Using Substitution

41. Common Logarithm

42. The Common Logarithm
The base-10 logarithm is called the common logarithm.
The common logarithm is usually written as logx.
If we can manage to make everything into log base 10, we can use our calculators to solve.

43. For Example….Solve

44. Solve:

45. Solve:

46. Solve:

47. Solve:

48. Section 3.3 Solving with Unlike Bases
Change of Base
Section 3.3
Solving with Unlike Bases

49. Change of Base
There is a way to write equivalent logarithmic expressions with different bases.
There is a formula to find the change of base.
Let’s derive the change of base formula…..

50. Let’s derive the change of Base Formula!

51. Change of Base Formula:

52. Example: Evaluate to the nearest hundredth.

53. Practice (Nearest 100th)

54. Practice (nearest 100th)

55. Practice (Nearest 100th)

56. Natural Log Equations

57. Practice (Nearest 100th)

58. Practice (Nearest 100th)

59. Practice (Nearest 100th)

60. Practice (Nearest 100th)