1 / 16

Activity 37

Activity 37. Logarithmic Functions (Section 5.2, pp. 398-405). Definition:. Let a be a positive number with a ≠ 1. The logarithmic function with base a, denoted by log a , is defined by. Properties of Logarithms (3 step proofs):. Let a be a positive number with a ≠ 1. Example 1:.

jeanne
Télécharger la présentation

Activity 37

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Activity 37 Logarithmic Functions (Section 5.2, pp. 398-405)

  2. Definition: Let a be a positive number with a ≠ 1. The logarithmic function with base a, denoted by loga, is defined by

  3. Properties of Logarithms (3 step proofs): Let a be a positive number with a ≠ 1

  4. Example 1: Change each exponential expression into an equivalent expression in logarithmic form:

  5. Example 2: Change each logarithmic expression into an equivalent expression in exponential form:

  6. Example 3: Evaluate each of the following expressions: Property 3 Property 3 Property 3

  7. Property 4 Property 3 Property 1

  8. Graphs of Logarithmic Functions:

  9. Example 4: Find the domain of the function and sketch its graph.

  10. Common Logarithms: The logarithm with base 10 is called the common logarithm and is denoted by omitting the base: log x := log10 (x).

  11. Example 5 (Bacteria Colony): A certain strain of bacteria divides every three hours. If a colony is started with 50 bacteria, then the time t (in hours) required for the colony to grow to N bacteria is given by Find the time required for the colony to grow to a million bacteria.

  12. Definition: Natural Logarithms The logarithm with base e is called the natural logarithm and is denoted by ln: ln x := loge x. We recall again that, by the definition of inverse functions, we have

  13. Properties of Natural Logarithms:

  14. Example 6: Evaluate each of the following expressions: Property 3 Property 3 Property 4

  15. Example 7: Graph the function

  16. Example 8: Find the domain of the function

More Related