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Logarithmic Functions and Graphs

Logarithmic Functions and Graphs. Objective. Sketch Logarithmic Graphs Use Log Properties. Relevance. Log functions are useful for modeling data that represent quantities that increase or decrease slowly .

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Logarithmic Functions and Graphs

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  1. Logarithmic Functions and Graphs

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

  23. 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 • The natural logarithmic function is the inverse of the natural exponential function

  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.

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