1 / 9

8.4 Logarithmic Functions

8.4 Logarithmic Functions. Relationship to Exponential Function. Recall the exponential function. The inverse is. Log b x = y. Definition of a Logarithm with base b. Let b and y be positive numbers and b  1. The logarithm of y with base b is denoted by Log b y and is defined as

vernon-beasley
Télécharger la présentation

8.4 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. 8.4 Logarithmic Functions

  2. Relationship to Exponential Function Recall the exponential function The inverse is Logb x = y

  3. Definition of a Logarithm with base b Let b and y be positive numbers and b  1. The logarithm of y with base b is denoted by Logb y and is defined as Logb y = x if and only if bx = y. Logarithmic Form Exponential Form Key: • Logb y and bx = y are equivalent • The base must be positive • The number that you are taking the log of must be positive  The value of the log is equal to the exponent.

  4. Change Logarithms to Exponential Form Log3 9 = 2 Log5 5 = 1 Log½4 = -2 Log19 1 = 0

  5. Change Exponential Equations to Logarithmic Form And Evaluate Example: Evaluate Log2 64 Evaluate Log25 5 Log6 1 Change to Exponential form

  6. Common Logarithm Log10 x = y is the common logarithm. Denoted simply as Log x Note: If you do not see a base written with the log, then the base is 10.

  7. Natural Logarithm Loge x = y is the natural log. Denoted as Ln y = x.

  8. Special Values of Logarithms Logb 1 = 0 because b0 = 1 Logb b = 1 because b1 = b Inverses Logb bx = x because g(f(x)) = x because f(g(x)) = x

  9. The Graph of Logarithmic Functionsy = logb (x - h) + k • x = h is the asymptote. • Domain x > h. • Range y is all real numbers. • If b > 1, the graph increases up to the right. • If 0 < b < 1, the graph reflects down. The graph decreases left to right.

More Related