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 ≈ … - 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”
e e e 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, ln 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 = e5 = x e7 = x
4. ln x = ln 10 = x 6. ln x =

7. Write each expression as a single logarithm.
3 ln 10 – ln ln ln ½ + ln x
9. 6ln 8 – 2ln ln 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 = e3x + 1= 5

10. ln x – 1 = ln x + 2 = 6

11. Continuous Compound Interest

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