Presentation is loading. Please wait.

Presentation is loading. Please wait.

10.5 Base e and Natural Logarithms 10.5. History The number e is a famous irrational number, and is one of the most important numbers in mathematics.

Similar presentations


Presentation on theme: "10.5 Base e and Natural Logarithms 10.5. History The number e is a famous irrational number, and is one of the most important numbers in mathematics."— Presentation transcript:

1 10.5 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 Calculating The value of (1 + 1/n) n approaches e as n gets bigger and bigger: n (1 + 1/n) n , , ,

4 Vocabulary natural base: the number e, which is found using the base rate of growth shared by all continually growing processes Used heavily in science to model quantities that grow & decay continuously natural base exponential function: an exponential function with base e

5 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

6 Ex 1 Use a calculator to estimate to four decimal places. Ex 2 Ex 3 Ex 4

7 Ex 5 Exponential logarithmic Write an equivalent equation in the other form. Ex 6 Writing Equivalent Expressions Ex 8 Ex 7

8 Inverse Properties

9 Ex 9 Evaluate Ex 11 Writing Equivalent Expressions Evaluate Ex 10 Evaluate Ex 12

10 Solving Equations Ex 13 Solve the following equations. Ex 14

11 Solving Equations Ex 15 Solve the following equations. Ex 16


Download ppt "10.5 Base e and Natural Logarithms 10.5. History The number e is a famous irrational number, and is one of the most important numbers in mathematics."

Similar presentations


Ads by Google