Logarithmic Functions

# Logarithmic Functions

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## Logarithmic Functions

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##### Presentation Transcript

1. Logarithmic Functions Dr. Johnny Duke Georgia Highlands College

2. Inverse In mathematics we like to be able to “undo” whatever has been done. For instance, a child learns to add, then learns to subtract which “undoes” addition. Once one learns to multiply, then division is learned to “undo” multiplication. These are inverse operations.

3. Inverse Functions

4. The Inverse of Exponential Functions

5. Practice

6. Definition Applied

7. Practice

8. stop

9. Graphs of Logarithmic Functions Dr. Johnny Duke

10. ..\gsp\log base 2.gsp

11. Transformations and Logarithmic Function Horizontal Shift, left one unit.

12. Transformations and Logarithmic Function Vertical Shift, up two units.

13. Transformations and Logarithmic Function Reflection through x-axis

14. Transformations and Logarithmic Function Reflection through y-axis

15. Transformations and Logarithmic Function Reflection through x-axis; vertical shift down 4 units; horizontal shift right 2 units.

16. Stop

17. Two Special Logarithmic Functions

18. Two Special Logarithmic Functions

19. Practice 1 -2 1.398 e 1.792 - .981

20. Change of Base Formula

21. Practice

22. stop

23. Properties of Logarithmic Functions Dr. Johnny Duke

24. Properties of logarithmic functions

25. Properties of logarithmic functions

26. More Properties of Logs

27. Expanding logarithmic expressions Property 1 Property 3 Property 2 Properties 1 and 3

28. Contracting logarithmic expressions Property 3 Property 1 Properties 3 and 2 Property 1

29. stop