1 / 12

6.7 – Base “ e” and Natural Logarithms

Uncover the secrets of the number "e" and natural logarithms, learn to solve equations, and understand their significance in mathematics.

india-walton
Download Presentation

6.7 – Base “ e” and 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. 6.7 – Base “e” and Natural Logarithms Objective – TSW solve equations that contain “e” and natural logarithms.

  2. What is this “e” business about ? “e” is a number like pi. - It is a non repeating, never ending decimal. - An irrational number. - e ≈ 2.71828… - e is the base of the natural log (ln)…just like 10 is the base of log.

  3. On your calculators…Let’s Practice Using “e” • e9 2. e3.4 3. 3e0.05 4. e1/4

  4. Why do we use “e” • Because in the natural log (ln) the base is e. ALL PROPERTIES of logarithms apply to natural logarithms. • Anytime you see ln…you can write loge  • For example: ln 3 means loge 3

  5. Let’s look at this “ln” business. • ln 99,999 2. ln 0.994 3. ln ½ 4. ln (-2) 5. ln (15)

  6. Examples…Write each exponential equation in logarithmic form or each logarithmic equation in exponential form. • ex = 8 2. e5 = x 3. e7 = x 4. ln x = 0.7741 5. ln 10 = x 6. ln x = 2.1438

  7. Write each expression as a single logarithm. • 3 ln 10 – ln 8 8. ln 40 + 2ln ½ + ln x 9. 6ln 8 – 2ln 4 10. 2ln 5 + 4ln 2 + ln 5y

  8. To Solve natural log equations: • Identify whether the equation is in log form or exponential form. • Get the “log/ln” portion by itself OR get the “exponential” portion by itself. • Rewrite into either log or exponential form. • Solve. • Check your answer. ***REMEMBER ln means loge***

  9. 11. ex+2 = 7 12. e3x + 1= 5

  10. 13. 3 ln x – 1 = 4 14. 2ln x + 2 = 6

  11. Continuous Compound Interest

  12. Homework… Pg. 529 #’s 1-14(all), 34, 36, 38 

More Related