1 / 12

3.3 Logarithmic Functions and Their Graphs

3.3 Logarithmic Functions and Their Graphs. The inverse of y = b x is y = log b x. Logarithmic Functions. log b 1 = 0 because b 0 = 1 ex) log 9 1 = log b b = 1 because b 1 = b ex) log 3 3 = log b b y = y because b y = b y ex) log 4 4 2 =

maris
Download Presentation

3.3 Logarithmic Functions and Their Graphs

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. 3.3 Logarithmic Functions and Their Graphs

  2. The inverse of y = bx is y = logbx Logarithmic Functions

  3. logb 1 = 0 because b0 = 1 ex) log9 1 = • logb b = 1 because b1 = b ex) log3 3 = • logbby = y because by = by ex) log4 42 = • blogbx = x because logbx = logbx ex) 7log73 = Logarithmic Basic Properties

  4. log232 • Log9√9 • log644 • 5log517 • log6(1/216) You Try! Evaluate Each Expression

  5. log 1 = 0 because 100 = 1 • log 10 = 1 because 101 = 10 • Log 10y = y because 10y = 10y ex) log 1 = 1000 • 10log x = x because log x = log x ex) 10log(.5) = Common Logarithms (Logs with base 10)

  6. log 9.43 ≈ Check: • log (-14) = You Try! • log 34.5 ≈ Check: Evaluate using calculator & Check

  7. Solving Logarithmic Equations • logx = 2 • Log5 x = -3 You Try! • logx = -1 • Log4 x = 6

  8. logex = lnx y = ln(x) is the inverse of the exponential function y = ex Natural Logarithms : Base e

  9. ln 1 = 0 because e0 = 1 • lne = 1 because e1 = e • lney = y because ey = ey ex) ln e3 = • elnx = x because lnx = lnx ex) eln6 = Natural logarithms

  10. lne-4 • ln 1/e • ln4√e • ln 4.05 ≈ Check: You Try! Evaluate:

  11. h(x) = ln (3 – x) g(x) = ln (x + 2) g(x) = 3 log x h(x) = 1 + log x

  12. Pg. 308-309: 4, 10, 14, 22, 24, 26, 32, 36, 44, 58 Homework

More Related