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The Natural Number, “e”

The Natural Number, “e”. Math 3 Standard MM3A3. Background:. Leonhard Euler, famous mathematician Lived during 1700’s Credited with many mathematical and scientific discoveries One of the most famous is “the natural number”, Now known as “e” Uses factorials . Factorials:.

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The Natural Number, “e”

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  1. The Natural Number,“e” Math 3 Standard MM3A3

  2. Background: • Leonhard Euler, famous mathematician • Lived during 1700’s • Credited with many mathematical and scientific discoveries • One of the most famous is “the natural number”, • Now known as “e” • Uses factorials

  3. Factorials: • Use the ! symbol • 5! = 5·4·3·2·1 = 120 • 10! = 10·9·8·7·6·5·4·3·2·1 = 3,628,800 • 0! = 1

  4. e is a series that uses factorials • Defined as: This is a convergent series. e is an irrational number.

  5. Your calculator knows what e is. • Use your calculator to evaluate each expression: • (round to three decimal places)

  6. You treat e like a variable. • Simplify each expression:

  7. The Natural Log (ln) • The natural log (ln) is the inverse operation of the natural number, e. • Just as the common logarithm “undoes” an exponential function, the natural logarithm (ln) “undoes” the natural number, e.

  8. Change of Base

  9. Change of Base Formula One property of logarithms is that a logarithm in any base can be rewritten as an equivalent logarithm in any other base. The formula is: This is known as the change of base formula and is especially useful when the base we are changing to is either 10 (the common log) or e (the natural logarithm) because most calculators have one or both of those logarithm functions built in.

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