6 7 Base e and Natural Logarithms Objective

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… - e is the base of the natural log (ln)…just like 10 is the base of log.

On your calculators… Let’s Practice Using “e” 1. e 9 e 1/4 2. e 3. 4 3. 3 e 0. 05 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

Let’s look at this “ln” business. 1. ln 99, 999 4. ln (-2) 2. ln 0. 994 5. ln (15) 3. ln ½

Examples…Write each exponential equation in logarithmic form or each logarithmic equation in exponential form. 1. ex = 8 4. ln x = 0. 7741 2. e 5 = x 3. e 7 = x 5. ln 10 = x 6. ln x = 2. 1438

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

To Solve natural log equations: Identify whether the equation is in log form or exponential form. 2. Get the “log/ln” portion by itself OR get the “exponential” portion by itself. 3. Rewrite into either log or exponential form. 4. Solve. 5. Check your answer. 1. ***REMEMBER ln means loge***

11. ex+2 = 7 12. e 3 x + 1= 5

13. 3 ln x – 1 = 4 14. 2 ln x + 2 = 6

Continuous Compound Interest

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