1 / 14

8.5 Natural Logarithms

8.5 Natural Logarithms. Natural Logarithms. Natural Logarithm: a natural log is a log with base e (the Euler Number) log e x or ln x. Natural Logarithms. Example: Use your calculator to find ln 3 Your calculator has a natural logarithm (Ln) key on it. ln 3 = 1.0986.

aiko
Download Presentation

8.5 Natural Logarithms

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. 8.5 Natural Logarithms

  2. Natural Logarithms Natural Logarithm:a natural log is a log with base e (the Euler Number) loge x or ln x

  3. Natural Logarithms Example: Use your calculator to find ln 3 Your calculator has a natural logarithm (Ln) key on it. ln 3 = 1.0986

  4. Ex. Graph f(x) = 3 – ln (x – 1) (enter it into your calculator exactly like that) x f(x)

  5. Ex. Graph f(x) = 3 – ln (x – 1) 1.25 x f(x)

  6. Ex. Graph f(x) = 3 – ln (x – 1) 1.25 1.5 2 3 4 5 6 x f(x)

  7. Ex. Graph f(x) = 3 – ln (x – 1) 1.25 1.5 2 3 4 5 6 4.38 x f(x)

  8. Ex. Graph f(x) = 3 – ln (x – 1) 1.25 1.5 2 3 4 5 6 4.38 3.69 3 2.31 1.90 1.611.39 x f(x)

  9. Ex. Graph f(x) = 3 – ln (x – 1) 1.25 1.5 2 3 4 5 6 4.38 3.69 3 2.31 1.90 1.611.39 x f(x)

  10. Ex. Graph f(x) = 3 – ln (x – 1) 1.25 1.5 2 3 4 5 6 4.38 3.69 3 2.31 1.90 1.611.39 f(x) = 3 – ln(x – 1) x f(x)

  11. Natural logarithms can be condensed/expanded using the properties of logarithms: Condense the expressions:a. ln 18 – ln 3b. 3ln x + ln y c. = ln (6) = ln (18/3) = ln x3y =ln 41/2 + ln (62/22) = ln (41/2 * 62/22) = ln (2* 36/4) = ln (2*9) = ln (18)

  12. Expand ln (4xy) = ln (4) + ln (x) + ln (y) ln (3x/y) = ln (3) + ln (x) – ln (y) ln (3x1/2y4) = ln (3) + 1/2ln (x) + 4ln (y)

  13. Solve When solving a ln problem treat it just like a log – get a single ln on each side and set the part in parenthesis equal to each other ln (4x) = ln (8) 4x = 8 4 4 x = 2 2ln (x) = ln (36) ln (x2) = ln (36) x2 = 36 ( )1/2 ( )1/2 x = 6

  14. Solve ln x – ln 10 = ln (8) ln (x/10) = ln (8) x/10= 8 x = 80

More Related