1. Inverse, Exponential, and Logarithmic Functions
Chapter 13
Inverse, Exponential, and Logarithmic Functions

2. Sect. 13.1 Inverse Functions
Only one-to-one functions have inverses.
Ex. 1

3. One-to-One Example continued

4. Use the horizontal line test to Determine if a Function is One-to-One
Ex. 2

5. Find the Inverse of a One-to-One Function
Ex. 3

6. Finding the Inverse of a One-to-One Function
Ex. 4

7. Finding the Relationship between a Function and Its Inverse
Ex. 5

8. Finding the Relationship between a Function and Its Inverse continued

9. Given the Graph of f(x), Graph f-1(x)
Ex. 6

10. Given the Equations of f(x) and f-1(x), Show That
Ex. 7

11. Sect. 13.2 Exponential Functions

12. Graph an Exponential Function

13. Another Exponential Graph

14. Graph an Exponential Function of the Form f(x) = ax+c

15. Define the Irrational Number e and Graph f(x) = ex

16. Ex. 5
Solve an Exponential Equation by Expressing Both Sides of the Equation with the Same Base

17. Solve an Exponential Equation by Expressing Both Sides of the Equation with the Same Base continued

18. Solve an Applied Problem Using a Given Exponential Function

19. Sect. 13.3 Logarithmic Functions

20. Rewrite an Equation in Logarithmic Form as an Equation in Exponential Form

21. Rewrite an Equation in Exponential Form as an Equation in Logarithmic Form

22. Solve a Logarithmic Equation of the Form logab = c
Ex. 3

23. Solve a Logarithmic Equation of the Form logab = c continued

24. Ex. 4
Evaluate a Logarithm

25. Evaluate Common Logarithms, and Solve Equations of the Form log b = c
Ex. 5

26. Solving a Logarithmic Equation
Ex. 6

27. Use the Properties logaa = 1and loga1 = 0
Ex. 7

28. Define and Graph a Logarithmic Function
Ex. 8

29. Graph a Logarithmic Function
Ex. 9

30. Another Logaritmic Graph
Ex. 10

31. Solve an Applied Problem Using a Given Logarithmic Equation
Ex. 11

32. Solve an Applied Problem Using a Given Logarithmic Equation continued

33. Sect. 13.4 Properties of Logarithms
Ex. 1 Using the Product Rule

34. Using the Product Rule continued
Ex. 2

35. Use the Quotient Rule for Logarithms
Ex. 3

36. More Examples of Using the Quotient Rule

37. Use the Power Rule for Logarithms
Ex. 5

38. Use the Power Rule for Logarithms cont.

39. Use the Properties logaax = x and alogax = x
Ex. 6

40. Combine the Properties of Logarithms to Rewrite Logarithmic Expressions

41. More Examples of Combining Properties

42. More Examples of Combining Properties
= 0.5(0.7782) =

43. Sect. 13.5 Common and Natural Logarithms and Change of Base

44. Evaluate Common Logarithms Using a Calculator
Ex. 2

45. Solve an Equation Containing a Common Logarithm
Ex. 3
Ex. 4

46. Solve an Applied Problem Given an Equation Containing a Common Logarithm
Ex. 5

47. Define a Natural Logarithm

48. Evaluate Natural Logarithms Without a Calculator
Ex. 6
Ex. 7

49. Solve an Equation Containing a Natural Logarithm
Ex. 8

50. Solve Applied Problems Using Exponential Functions
Definition: Compound Interest: The amount of money, A, in dollars, in an account after t years is given by
where P (the principal ) is the amount of money (in dollars) deposited in the account, r is the annual interest rate, and n is theniumber of times the interest is compounded per year.

51. Continuous Compounding
Ex. 10

52. Use the Change-of-Base Formula
Ex. 11

53. Sect. 13.6 Solving Exponential and Logarithmic Equations
Ex. 1 Solve by taking ln of both sides

54. Solving an Exponential Equation
ln5

55. Another Example of Solving an Exponential Equation

56. Solve Logarithmic Equations Using the Properties of Logarithms
Ex. 4

57. Solve Logarithmic Equations Using the Properties of Logarithms continued

58. Solve an Equation Where One Term Does Not Contain a Logarithm
Ex. 5

59. Solve Applied Problems Involving Exponential Functions Using a Calculator

60. Doubling Time
Ex. 7

61. Solve an Applied Problem Involving Exponential Growth or Decay

62. Solve an Applied Problem Involving Exponential Growth or Decay continued