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10.5 Base e and Natural Logarithms 10.5 Notes # ___.

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Presentation on theme: "10.5 Base e and Natural Logarithms 10.5 Notes # ___."— Presentation transcript:

1 10.5 Base e and Natural Logarithms 10.5 Notes # ___

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 2.7182818284590452353602874713527... 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 12.00000 22.25000 52.48832 102.59374 1002.70481 1,0002.71692 10,0002.71815 100,0002.71827

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

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

8 Ex 5 Write an equivalent logarithmic equation. Ex 6 Writing Equivalent Expressions Write an equivalent logarithmic equation.

9 Ex 7 Write an equivalent exponential equation. Ex 8 Writing Equivalent Expressions Write an equivalent exponential equation.

10 Inverse Properties

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

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


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