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8.3-4 – Logarithmic Functions

8.3-4 – Logarithmic Functions. Logarithm Functions. Logarithm Functions If log b x = y ,. Logarithm Functions If log b x = y , then b y = x. Logarithm Functions If log b x = y , then b y = x . Ex. 1 Write the following in exponential form. a. log 8 1 = 0 .

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8.3-4 – Logarithmic Functions

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  1. 8.3-4 – Logarithmic Functions

  2. Logarithm Functions

  3. Logarithm Functions If logbx = y,

  4. Logarithm Functions If logbx = y, then by = x.

  5. Logarithm Functions If logbx = y, then by = x. Ex. 1 Write the following in exponential form. a. log81 = 0

  6. Logarithm Functions If logbx = y, then by = x. Ex. 1 Write the following in exponential form. a. log81 = 0 logbx = y

  7. Logarithm Functions If logbx = y, then by = x. Ex. 1 Write the following in exponential form. a. log81 = 0 logbx = y

  8. Logarithm Functions If logbx = y, then by = x. Ex. 1 Write the following in exponential form. a. log81 = 0 logbx = y

  9. Logarithm Functions If logbx = y, then by = x. Ex. 1 Write the following in exponential form. a. log81 = 0 logbx = y

  10. Logarithm Functions If logbx = y, then by = x. Ex. 1 Write the following in exponential form. a. log81 = 0 logbx = y by = x

  11. Logarithm Functions If logbx = y, then by = x. Ex. 1 Write the following in exponential form. a. log81 = 0 logbx = y by = x 80 = 1

  12. Logarithm Functions If logbx = y, then by = x. Ex. 1 Write the following in exponential form. a. log81 = 0 logbx = y by = x 80 = 1

  13. Logarithm Functions If logbx = y, then by = x. Ex. 1 Write the following in exponential form. a. log81 = 0b. log2(1/16) = -4 logbx = y by = x 80 = 1

  14. Logarithm Functions If logbx = y, then by = x. Ex. 1 Write the following in exponential form. a. log81 = 0b. log2(1/16) = -4 logbx = y 2-4 = 1/16 by = x 80 = 1

  15. Logarithm Functions If logbx = y, then by = x. Ex. 1 Write the following in exponential form. a. log81 = 0b. log2(1/16) = -4 logbx = y 2-4 = 1/16 by = x 80 = 1 Ex. 2 Write the following in logarithmic form. a. 103 = 1000 b. 27⅓ = 3

  16. Logarithm Functions If logbx = y, then by = x. Ex. 1 Write the following in exponential form. a. log81 = 0b. log2(1/16) = -4 logbx = y 2-4 = 1/16 by = x 80 = 1 Ex. 2 Write the following in logarithmic form. a. 103 = 1000 b. 27⅓ = 3 by = x

  17. Logarithm Functions If logbx = y, then by = x. Ex. 1 Write the following in exponential form. a. log81 = 0b. log2(1/16) = -4 logbx = y 2-4 = 1/16 by = x 80 = 1 Ex. 2 Write the following in logarithmic form. a. 103 = 1000 b. 27⅓ = 3 by = x

  18. Logarithm Functions If logbx = y, then by = x. Ex. 1 Write the following in exponential form. a. log81 = 0b. log2(1/16) = -4 logbx = y 2-4 = 1/16 by = x 80 = 1 Ex. 2 Write the following in logarithmic form. a. 103 = 1000 b. 27⅓ = 3 by = x logbx = y

  19. Logarithm Functions If logbx = y, then by = x. Ex. 1 Write the following in exponential form. a. log81 = 0b. log2(1/16) = -4 logbx = y 2-4 = 1/16 by = x 80 = 1 Ex. 2 Write the following in logarithmic form. a. 103 = 1000 b. 27⅓ = 3 by = x logbx = y log101000 = 3

  20. Logarithm Functions If logbx = y, then by = x. Ex. 1 Write the following in exponential form. a. log81 = 0b. log2(1/16) = -4 logbx = y 2-4 = 1/16 by = x 80 = 1 Ex. 2 Write the following in logarithmic form. a. 103 = 1000 b. 27⅓ = 3 by = xlog273 = ⅓ logbx = y log101000 = 3

  21. Ex. 3 Evaluate each expression. a. log264 b. log164

  22. Ex. 3 Evaluate each expression. a. log264 b. log164 log264 = y

  23. Ex. 3 Evaluate each expression. a. log264 b. log164 log264 = y logbx = y

  24. Ex. 3 Evaluate each expression. a. log264 b. log164 log264 = y logbx = y by = x

  25. Ex. 3 Evaluate each expression. a. log264 b. log164 log264 = y logbx = y by = x 2y = 64

  26. Ex. 3 Evaluate each expression. a. log264 b. log164 log264 = y logbx = y by = x 2y = 64 2y = 26

  27. Ex. 3 Evaluate each expression. a. log264 b. log164 log264 = y logbx = y by = x 2y = 64 2y = 26 y = 6

  28. Ex. 3 Evaluate each expression. a. log264 b. log164 log264 = y logbx = y by = x 2y = 64 2y = 26 y = 6

  29. Ex. 3 Evaluate each expression. a. log264 b. log164 log264 = y log164 = y logbx = y 16y = 4 by = x (42)y = 4 2y = 64 42y = 41 2y = 26 2y = 1 y = 6 y = ½

  30. Ex. 4 Solve each equation. a. log9x = 2 b. logb121 = 2

  31. Ex. 4 Solve each equation. a. log9x = 2 b. logb121 = 2 logbx = y

  32. Ex. 4 Solve each equation. a. log9x = 2 b. logb121 = 2 logbx = y by = x

  33. Ex. 4 Solve each equation. a. log9x = 2 b. logb121 = 2 logbx = y by = x 92 = x

  34. Ex. 4 Solve each equation. a. log9x = 2 b. logb121 = 2 logbx = y by = x 92 = x 81 = x

  35. Ex. 4 Solve each equation. a. log9x = 2 b. logb121 = 2 logbx = y by = x 92 = x 81 = x

  36. Ex. 4 Solve each equation. a. log9x = 2 b. logb121 = 2 logbx = yb2 = 121 by = xb = ±11 92 = x 81 = x

  37. Ex. 4 Solve each equation. a. log9x = 2 b. logb121 = 2 logbx = yb2 = 121 by = xb = ±11 92 = xb = +11 81 = x *b cannot be neg.!

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