1. Logarithmic Functions

2. Objectives To write exponential equations in logarithmic form. To use properties of logarithms to expand and condense logarithmic expressions. Don’t be afraid of logs!

3. Logarithmic Functions Key to understanding logarithms: A logarithm is an exponent! Exponent Base Argument

4. Logarithmic Functions Exponential Form Logarithmic Form

5. Logarithmic Functions Evaluate:

6. Evaluate:

7. Evaluate:

8. Evaluate:

9. Evaluate:

10. Evaluate:

11. Evaluate:

12. Special Bases Common log Natural log

13. Natural Logarithm Evaluate:

14. Properties of Logarithms

15. Expand:

16. Expand: ln does not distribute!

17. Properties of Logarithms Expand:

18. Expand:

19. Combine:

20. Combine:

21. Combine:

22. Combine:

23. Combine:

24. Solving Equations Using Logs Solve:Solve:

25. Solve:Solve:

26. Solve:Solve:

27. Solve:Solve:

28. Using Logarithms Suppose you deposit money into an account whose annual interest rate is 4% compounded continuously. How long will it take for the money to double?

29. Using Logarithms Chris wants to buy a car. It costs $30,000, and he only has $27,000. If he invests it in a bank account at 6% interest compounded quarterly, how long will he have to wait before it matures to $30,000?

30. Logarithmic Functions Consider:

32. The inverse of a logarithmic function is an exponential function.

33. Logarithmic Functions (red)

34. Conclusion A logarithm indicates the exponent to which you raise a certain base in order to produce a given value. The inverse of logarithmic function is an exponential function. Logs to the base 10 are written without a base. Logs to the base e are indicated by the symbol ln.