1. Logarithmic Functions and Graphs

2. Sketch Logarithmic Graphs Use Log Properties
Objective
Sketch Logarithmic Graphs Use Log Properties

3. Relevance
Log functions are useful for modeling data that represent quantities that increase or decrease slowly. For example, a log function can model the minimum required ventilation rates in public school classrooms.

4. Warm Up – Make Some Observations

5. Annually Monthly Quarterly Continuously
Warm Up - If $5,000 is invested at an interest rate of 5% per year, find the amount of the investment at the end of 5 years for the following compounding methods:
Annually
Monthly
Quarterly
Continuously

6. Annually:
Monthly:

7. Quarterly:
Continuously

8. Warm Up
Solve:
Find the Vertex:

9. Logarithmic Functions

10. Logarithmic Function It’s the inverse of the exponential function
Switch the x’s and the y’s!

11. Logarithmic Function
Used to find unknown exponents in exponential models.
Logs define many measurement scales in the sciences:
1) ph
2) decibal
3) Richter scale

12. For any positive base b, where b≠1: bx = y if and only if x = logby
Exponential Form
Logarithmic Form

13. Write in logarithmic form.

14. Write in logarithmic form.

15. Write in logarithmic form.

16. Write in exponential form.

17. Write in exponential form.

18. Write in exponential form.

19. Graphing Log Functions

20. Graph:
Is the inverse of
Domain:
Range:
Domain:
Range:

21. Graph:
Up 3 from previous example!
Domain:
Range:

22. Left 4 from Original Example!
Graph:
Left 4 from Original Example!
Domain:
Range:

23. Right 2 from Original Example!
Graph:
Right 2 from Original Example!
Domain:
Range:

24. Graph:
Reflected over y-axis.
Domain:
Range:

25. Graph:
Reflected over x-axis.
Domain:
Range:

26. Solving Log Functions

27. Find the value of x.

28. Find the value of x.

29. Find the value of x.

30. Find the value of x.

31. Find the value of x.

32. Find the value of x.

33. Find the value of x.

34. Find the value of x.

35. Find the value of x.

36. Natural Log

37. Natural log

38. The Natural Logarithmic Function
is the inverse of the natural exponential function
Function
Inverse

39. Write in logarithmic form.

40. Write in exponential form.

41. Find the value of x.

42. Using Calculator

43. Solve

44. Find to the nearest thousandth – using the calculator.

45. Find to the nearest thousandth – using the calculator.

46. Find to the nearest thousandth – using the calculator.