1. Base e and Natural Logarithms 10.5
Notes # ___
Base e and Natural Logarithms 10.5

2. History
The number e is a famous irrational number, and is one of the most important numbers in mathematics. The first few digits are
It is often called Euler's number after Leonhard Euler. e is the base of the natural logarithms (invented by John Napier).

3. The value of (1 + 1/n)n approaches e as n gets bigger and bigger: n
Calculating
The value of (1 + 1/n)n approaches e as n gets bigger and bigger: n
(1 + 1/n)n 1 2 5 10
100
1,000
10,000
100,000

4. Vocabulary natural base: the number e, which is found using
It is the base rate of growth shared by all continually growing processes
natural base exponential function: an exponential function with base e

5. Use a calculator to estimate to four decimal places.
Ex 1
Use a calculator to estimate to four decimal places.
Ex 2
Use a calculator to estimate to four decimal places.

6. Vocabulary natural logarithm: a logarithm with base e
The natural log gives you the time needed to reach a certain level of growth.
natural logarithmic function: the inverse of the natural base exponential function

7. Use a calculator to estimate to four decimal places.
Ex 3
Use a calculator to estimate to four decimal places.
Ex 4
Use a calculator to estimate to four decimal places.

8. Writing Equivalent Expressions
Write an equivalent logarithmic equation.
Ex 6
Write an equivalent logarithmic equation.

9. Writing Equivalent Expressions
Write an equivalent exponential equation.
Ex 8
Write an equivalent exponential equation.

10. Inverse Properties

11. Writing Equivalent Expressions
Evaluate
Evaluate
Ex 11
Ex 12
Evaluate
Evaluate

12. Solving Equations
Ex 13
Solve

13. Solving Equations
Ex 14
Solve

14. Solving Equations
Ex 15
Solve

15. Solving Equations
Ex 16
Solve

16. Solving Inequalities
Ex 17
Solve

17. Solving Inequalities
Ex 18
Solve