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Base e and Natural Logarithms 10.5

Base e and Natural Logarithms 10.5

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Base e and Natural Logarithms 10.5

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  1. Base e and Natural Logarithms10.5 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 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 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 Use a calculator to estimate to four decimal places.

  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 Use a calculator to estimate to four decimal places.

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

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

  10. Inverse Properties

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

  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