1 / 5

9.3 Logarithmic Functions ( Day 2)

9.3 Logarithmic Functions ( Day 2). Recall the graphs of y = log b x : f ( x ) = log b x has the y -axis as its asymptote The y -axis is x = 0, so if we change the function to f ( x ) = log b (a x + c), then a x + c = 0 is the asymptote.

deiter
Download Presentation

9.3 Logarithmic Functions ( Day 2)

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. 9.3 Logarithmic Functions (Day 2)

  2. Recall the graphs of y = logbx: f (x) = logbx has the y-axis as its asymptote The y-axis is x = 0, so if we change the function to f (x)= logb(ax + c), then ax + c = 0 is the asymptote. The x-int is found by letting y = 0 & y-int is when x = 0 Ex 1) Find the asymptote and x- & y-int of h(x) = log (3x + 10) asymptote: 3x + 10 = 0 3x = –10 b > 1 0 < b < 1 y-int: y = log (3(0) + 10) y = log (10) 10y = 101 y = 1 x-int: 0 = log (3x + 10) 100 = 3x + 10 1 = 3x + 10 –9 = 3x x = –3 (0, 1) (–3, 0)

  3. We can use our calculators to estimate logs  we will round to a typical 4 decimal places. Ex 2) Which is wrong? log 510 = 2.7076 b) ln 70.5 = 4.2556 c) log 0.03 = 1.5229 Change of Base Formula: typically: which is written as (used in calculus a lot!) Ex 3) Calculate log2 7 Half Class: Half Class: both 2.8074

  4. Logarithms are used to model a wide variety of problems. For example, magnitude of sound, Decibels, is where I = intensity of sound & I0 is intensity of the threshold of hearing, which is 10–16 W/cm2 Ex 4) Determine the loudness of each sound to the nearest decibel. a) Whisper: I = 3.16 × 10–15 b) A subway train: I = 5.01 × 10–7 Another application is the Richter Scale to measure the magnitude of earthquakes. x0 is magnitude of zero-level earthquake w/ reading of 0.001 mm x is seismographic reading of quake

  5. Homework #904 Pg 458 #1–9 odd, 10, 13, 17, 20, 24, 27–29, 32–34, 36, 38, 39, 41, 43–45

More Related