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The Logarithm as an Integral

The Logarithm as an Integral. Lesson 5.9. Previous Definition of ln x. In Lesson 2.4 we defined ln x as the inverse of e x Consider an alternative definition View geometric interpretation spreadsheet The area under the curve from 1 to x. Properties of a Logarithm. When we define

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The Logarithm as an Integral

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  1. The Logarithm as an Integral Lesson 5.9

  2. Previous Definition of ln x • In Lesson 2.4 we defined ln x as the inverse of ex • Consider an alternative definition • View geometric interpretation spreadsheet • The area under the curve from 1 to x

  3. Properties of a Logarithm • When we define • The propertiesof logarithms still hold • Properties

  4. Natural Exponential Function • This alternative definition of ln x starts with ln x • Now we use it to define ex or E(x) • Properties:

  5. Assignment • Lesson 5.9 • Page 345 • Exercises 2 & 3 • If you wish, you may do #2 on a spreadsheet • A column of x values • A column of f(x) = 1/x • A column with 4*f(x) and 2*f(x) and f(a) and f(b) • Etc.

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