1 / 13

Logarithmic Functions

Logarithmic Functions. Think about it…. Is there an inverse of f(x)=a x The function is 1-1 (and passes the horizontal line test) then the function has an inverse The inverse is called the logarithmic function f -1 The base would be a. Definition. a is a positive number where a≠1

vail
Download Presentation

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. Logarithmic Functions

  2. Think about it… • Is there an inverse of f(x)=ax • The function is 1-1 (and passes the horizontal line test) then the function has an inverse • The inverse is called the logarithmic function f-1 • The base would be a

  3. Definition • a is a positive number where a≠1 • The logarithmic function with base a is denoted by: • And is defined by

  4. Forms • We can use this definition to switch between exponential form and logarithmic form exponent exponent base base

  5. Evaluating Logarithms • Remember to switch between forms • If one form is true then so is the other • Evaluate log10100,000=5 b/c 105=100,000 log28=3 b/c 23=8 log2(1/8)=-3 b/c 2-3=1/8

  6. Graphing Logarithmic Functions • Make a table of values • Ex: f(x)=log2x remember….2y=x

  7. Translations of logarithms • Same rules apply!! • Vertical • Horizontal • Reflection over the x axis • Reflection over the y axis

  8. Properties of Logarithms • loga1=0 • logaa=1 • Logaax=x • alogax=x

  9. Common Logs • A log with base of 10 is called the common log • logx=log10x • Follow the same properties

  10. Natural Logs • Logarithm with base e • ln x=logex • Properties: • ln 1=0 • lne=1 • ln ex=x • elnx=x

  11. Graphing Natural Logs f(x)=ln(x) • Make a table of values

  12. Translating natural log function • Vertical Translations • ln(x)±c • Horizontal Translations • ln(x±c) • Vertical Stretch/Compression • cln(x) • Horizontal Stretch/Compression • ln(cx) • Reflection over the x-axis • -ln(x) • Reflection over the y-axis • ln(-x) • Reflection over y=x • x=ln(y) ex=y

  13. Practice/Hw • Practice • 8-3: p.108 # 1, 5, 13, 21, 30, 42, 50 • Hw • P. 405 #1-28

More Related