1. 8.3-4 – Logarithmic Functions

2. Logarithm Functions

3. If log b x = y,

4. Logarithm Functions If log b x = y, then b y = x.

5. Logarithm Functions If log b x = y, then b y = x. Ex. 1 Write the following in exponential form. a. log 8 1 = 0

6. Logarithm Functions If log b x = y, then b y = x. Ex. 1 Write the following in exponential form. a. log 8 1 = 0 log b x = y

7. Logarithm Functions If log b x = y, then b y = x. Ex. 1 Write the following in exponential form. a. log 8 1 = 0 log b x = y

8. Logarithm Functions If log b x = y, then b y = x. Ex. 1 Write the following in exponential form. a. log 8 1 = 0 log b x = y

9. Logarithm Functions If log b x = y, then b y = x. Ex. 1 Write the following in exponential form. a. log 8 1 = 0 log b x = y

10. Logarithm Functions If log b x = y, then b y = x. Ex. 1 Write the following in exponential form. a. log 8 1 = 0 log b x = y b y = x

11. Logarithm Functions If log b x = y, then b y = x. Ex. 1 Write the following in exponential form. a. log 8 1 = 0 log b x = y b y = x 8 0 = 1

12. Logarithm Functions If log b x = y, then b y = x. Ex. 1 Write the following in exponential form. a. log 8 1 = 0 log b x = y b y = x 8 0 = 1

13. Logarithm Functions If log b x = y, then b y = x. Ex. 1 Write the following in exponential form. a. log 8 1 = 0 b. log 2 (1/16) = -4 log b x = y b y = x 8 0 = 1

14. Logarithm Functions If log b x = y, then b y = x. Ex. 1 Write the following in exponential form. a. log 8 1 = 0 b. log 2 (1/16) = -4 log b x = y 2 -4 = 1/16 b y = x 8 0 = 1

15. Logarithm Functions If log b x = y, then b y = x. Ex. 1 Write the following in exponential form. a. log 8 1 = 0 b. log 2 (1/16) = -4 log b x = y 2 -4 = 1/16 b y = x 8 0 = 1 Ex. 2 Write the following in logarithmic form. a. 10 3 = 1000b. 27 ⅓ = 3

16. Logarithm Functions If log b x = y, then b y = x. Ex. 1 Write the following in exponential form. a. log 8 1 = 0 b. log 2 (1/16) = -4 log b x = y 2 -4 = 1/16 b y = x 8 0 = 1 Ex. 2 Write the following in logarithmic form. a. 10 3 = 1000b. 27 ⅓ = 3 b y = x

17. Logarithm Functions If log b x = y, then b y = x. Ex. 1 Write the following in exponential form. a. log 8 1 = 0 b. log 2 (1/16) = -4 log b x = y 2 -4 = 1/16 b y = x 8 0 = 1 Ex. 2 Write the following in logarithmic form. a. 10 3 = 1000b. 27 ⅓ = 3 b y = x

18. Logarithm Functions If log b x = y, then b y = x. Ex. 1 Write the following in exponential form. a. log 8 1 = 0 b. log 2 (1/16) = -4 log b x = y 2 -4 = 1/16 b y = x 8 0 = 1 Ex. 2 Write the following in logarithmic form. a. 10 3 = 1000b. 27 ⅓ = 3 b y = x log b x = y

19. Logarithm Functions If log b x = y, then b y = x. Ex. 1 Write the following in exponential form. a. log 8 1 = 0 b. log 2 (1/16) = -4 log b x = y 2 -4 = 1/16 b y = x 8 0 = 1 Ex. 2 Write the following in logarithmic form. a. 10 3 = 1000b. 27 ⅓ = 3 b y = x log b x = y log 10 1000 = 3

20. Logarithm Functions If log b x = y, then b y = x. Ex. 1 Write the following in exponential form. a. log 8 1 = 0 b. log 2 (1/16) = -4 log b x = y 2 -4 = 1/16 b y = x 8 0 = 1 Ex. 2 Write the following in logarithmic form. a. 10 3 = 1000b. 27 ⅓ = 3 b y = x log 27 3 = ⅓ log b x = y log 10 1000 = 3

21. Ex. 3 Evaluate each expression. a. log 2 64 b. log 16 4

22. Ex. 3 Evaluate each expression. a. log 2 64 b. log 16 4 log 2 64 = y

23. Ex. 3 Evaluate each expression. a. log 2 64 b. log 16 4 log 2 64 = y log b x = y

24. Ex. 3 Evaluate each expression. a. log 2 64 b. log 16 4 log 2 64 = y log b x = y b y = x

25. Ex. 3 Evaluate each expression. a. log 2 64 b. log 16 4 log 2 64 = y log b x = y b y = x 2 y = 64

26. Ex. 3 Evaluate each expression. a. log 2 64 b. log 16 4 log 2 64 = y log b x = y b y = x 2 y = 64 2 y = 2 6

27. Ex. 3 Evaluate each expression. a. log 2 64 b. log 16 4 log 2 64 = y log b x = y b y = x 2 y = 64 2 y = 2 6 y = 6

28. Ex. 3 Evaluate each expression. a. log 2 64 b. log 16 4 log 2 64 = y log b x = y b y = x 2 y = 64 2 y = 2 6 y = 6

29. Ex. 3 Evaluate each expression. a. log 2 64 b. log 16 4 log 2 64 = y log 16 4 = y log b x = y 16 y = 4 b y = x (4 2 ) y = 4 2 y = 64 4 2y = 4 1 2 y = 2 6 2y = 1 y = 6 y = ½

30. Ex. 4 Solve each equation. a. log 9 x = 2b. log b 121 = 2

31. Ex. 4 Solve each equation. a. log 9 x = 2b. log b 121 = 2 log b x = y

32. Ex. 4 Solve each equation. a. log 9 x = 2b. log b 121 = 2 log b x = y b y = x

33. Ex. 4 Solve each equation. a. log 9 x = 2b. log b 121 = 2 log b x = y b y = x 9 2 = x

34. Ex. 4 Solve each equation. a. log 9 x = 2b. log b 121 = 2 log b x = y b y = x 9 2 = x 81 = x

35. Ex. 4 Solve each equation. a. log 9 x = 2b. log b 121 = 2 log b x = y b y = x 9 2 = x 81 = x

36. Ex. 4 Solve each equation. a. log 9 x = 2b. log b 121 = 2 log b x = y b 2 = 121 b y = x b = ±11 9 2 = x 81 = x

37. Ex. 4 Solve each equation. a. log 9 x = 2b. log b 121 = 2 log b x = y b 2 = 121 b y = x b = ±11 9 2 = x b = +11 81 = x *b cannot be neg.!