1 / 19

Lesson 5-6: Logarithms and Logarithmic Functions

Lesson 5-6: Logarithms and Logarithmic Functions. Advanced Math Topics. Key Concept. Logarithms with base b Read: “Log of x base b is y”. Key Concepts. Common Logarithm: log 10 can just be written log Log 100 is the same as log 10 100

judson
Download Presentation

Lesson 5-6: Logarithms and Logarithmic Functions

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. Lesson 5-6: Logarithms and Logarithmic Functions Advanced Math Topics

  2. Key Concept • Logarithms with base b • Read: “Log of x base b is y”

  3. Key Concepts • Common Logarithm: log10 can just be written log • Log 100 is the same as log10 100 • There is a button on your calculator for log you can only use it when you are dealing with base 10! • Natural Logarithm: loge is called the natural log and is written ln • Loge1 is the same as the ln 1 • There is a button on your calculator for ln you can use this anytime you see ln in a problem!

  4. Logarithmic to Exponential Form 1. log6 216 = 3 2. log4 1 = 0 3. log3 81 = 4 4. ln e2 = 2 5. log 40 = 1.6

  5. Exponential to Logarithmic Form 6. y = log10 100 7. log2 0.25 = y 8. log5 625 9. log10 0.001

  6. Write each equation in logarithmic form 10. 29 = 512 11. 0.04-3/2 = 125 12. e5 =148.4

  7. Evaluate Logarithmic Expressions 13. log 43 14. log 4300 15. ln 0.05 16. log2 32 17. log5 1/125 18. log11 1/121

  8. Solve 19. logx 25 = 2 20. logx 9/100 = -2 20. logx = 1/2

  9. Characteristics of Logarithmic Functions • 1. Inverse of the exponential function y=bx • 2.Continous and one-to-one • 3. Domain is all positive real numbers • 4. y-axis is an asymptote • 5. Range is ARN • 6. Contains (1,0), so x-intercept is 1

  10. Helpful Hint • Since exponential and logarithmic functions are inverses if the bases are the same they “undo” each other…

  11. Logarithmic Equations • Property of Equality • If b is a positive number other than 1, then if and only if x = y.

  12. Example 4 • Solve

  13. Example 5 • Solve

  14. Example 6 • Solve

  15. Example 7 • Solve

  16. Example 8 • Solve

  17. Example 9 • Solve

  18. Example 10 • Solve

  19. Example 11 • Solve

More Related