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6.7 – Base “ e” and Natural Logarithms

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

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6.7 – Base “ e” and Natural Logarithms

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  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 

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