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8.4 Logarithmic Functions

8.4 Logarithmic Functions. Standards 11, 14. Goal 1: Evaluate logarithmic functions Goal 2: Graph logarithmic functions. When is it used?. Tornado speeds. Earthquake energy . Goal 1: Evaluate logarithmic functions. Logs. We know that . and. but what is x when. ?.

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8.4 Logarithmic Functions

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  1. 8.4 Logarithmic Functions Standards 11, 14 • Goal 1: Evaluate logarithmic functions • Goal 2: Graph logarithmic functions

  2. When is it used? Tornado speeds Earthquake energy Goal 1: Evaluate logarithmic functions

  3. Logs We know that and but what is x when ? Definition of logarithm with base b Goal 1: Evaluate logarithmic functions

  4. Examples Rewrite the exponential form to logarithmic form or vice versa. Goal 1: Evaluate logarithmic functions

  5. White boards Rewrite the exponential form to logarithmic form or vice versa. Goal 1: Evaluate logarithmic functions

  6. Evaluating Log Expressions 3 to what power is 81? 5 to what power is 0.04? 1/2 to what power is 8? Goal 1: Evaluate logarithmic functions

  7. White Boards Goal 1: Evaluate logarithmic functions

  8. Common & Natural Logs Common Log log with base 10 Natural Log log with base e Goal 1: Evaluate logarithmic functions

  9. Notes Evaluating Log & ln Expressions Goal 1: Evaluate logarithmic functions

  10. White Boards Evaluating Log & ln Expressions Goal 1: Evaluate logarithmic functions

  11. Review Inverses Inverses: +/- x/÷ square, square root Goal 2: Graph Log Functions

  12. Notes Log Inverses Exponential functions and logarithmic functions undo each other Goal 2: Graph Log Functions

  13. Notes Evaluate using Log Inverses Shortcut Simplify the expression. Original Problem make = y log and base cancel Rewrite in log form logs cancel out Goal 2: Graph Log Functions

  14. Notes Evaluate using Log Inverses Shortcut Simplify the expression. Original Problem make = y Rewrite in exponential form bases cancel out Goal 2: Graph Log Functions

  15. White Boards Evaluate using Log Inverses

  16. Notes Log Inverses Find the inverse of the function. Original problem Switch x and y Rewrite in exponential form; isolate y The inverse of is Goal 2: Graph Log Functions

  17. Notes Log Inverses Find the inverse of the function. Original problem Switch x and y Rewrite in exponential form; isolate y ; The inverse of is Goal 2: Graph Log Functions

  18. Log Inverses: White boards Find the inverse of the function. Goal 2: Graph Log Functions

  19. Graphing Logs h: the line x = h is the VERTICAL asymptote b: if b > 1, then graph moves up and right (⟰,⇛) if 0<b < 1, then graph moves down and right (⟱,⇛) (⟱,⇛) (⟰,⇛) Goal 2: Graph Log Functions

  20. Graph Logs Graph the function. State the domain and range. 0 < b < 1 down and right; almost flattens asymptote x = 0 Goal 2: Graph Log Functions

  21. Graph Logs Graph the function. State the domain and range. b > 0 up and right; almost flattens asymptote x = -2 Goal 2: Graph Log Functions

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