Base e and Natural Logarithms 10.5

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Base e and Natural Logarithms 10.5 - PowerPoint PPT Presentation

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. The first few digits are 2.7182818284590452353602874713527 ...

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Base e and Natural Logarithms10.5

History

The number e is a famous irrational number, and is one of the most important numbers in mathematics. The first few digits are

2.7182818284590452353602874713527...

It is often called Euler's numberafter Leonhard Euler. e is the base of the natural logarithms (invented by John Napier).

Calculating

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

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

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

Ex 1

Ex 2

Use a calculator to estimate to four decimal places.

Ex 3

Ex 4

Writing Equivalent Expressions

Ex 5

Exponential logarithmic

Write an equivalent equation in the other form.

Ex 6

Ex 7

Ex 8

Writing Equivalent Expressions

Ex 9

Ex 10

Evaluate

Evaluate

Ex 11

Ex 12

Evaluate

Evaluate

Solving Equations

Solve the following equations.

Ex 13

Ex 14

Solving Equations

Solve the following equations.

Ex 15

Ex 16