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Base e and Natural Logarithms 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. The first few digits are 2.7182818284590452353602874713527 ...

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Base e and Natural Logarithms 10.5

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  1. Base e and Natural Logarithms10.5

  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 2.7182818284590452353602874713527... It is often called Euler's numberafter 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:

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

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

  8. Inverse Properties

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

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

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

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