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Section 4.4 Laws of Logarithms

Chapter 4 – Exponential and Logarithmic Functions. Section 4.4 Laws of Logarithms. Example. Find the pattern. The Product Rule. Let a be a positive number with a  1. Let A , B , and C be any real number with A > 0 and B > 0.

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Section 4.4 Laws of Logarithms

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  1. Chapter 4 – Exponential and Logarithmic Functions Section 4.4 Laws of Logarithms 4.4 - Laws of Logarithms

  2. Example Find the pattern. 4.4 - Laws of Logarithms

  3. The Product Rule • Let a be a positive number with a 1. Let A, B, and C be any real number with A > 0 and B > 0. • This means, the logarithm of a product of numbers is the sum of logarithms of the numbers. 4.4 - Laws of Logarithms

  4. Example Find the pattern. 4.4 - Laws of Logarithms

  5. The Quotient Rule • Let a be a positive number with a 1. Let A, B, and C be any real number with A > 0 and B > 0. • This means, the logarithm of a quotient of numbers is the difference of logarithms of the numbers. 4.4 - Laws of Logarithms

  6. Example Find the pattern. 4.4 - Laws of Logarithms

  7. The Power Rule • Let a be a positive number with a 1. Let A, B, and C be any real number with A > 0 and B > 0. • This means, the logarithm of a power of a number is the exponent times the logarithm of the number. 4.4 - Laws of Logarithms

  8. Change of Base 4.4 - Laws of Logarithms

  9. Compress the Expression • Compress the expression to a single logarithm. 4.4 - Laws of Logarithms

  10. Expand the Expression • Expand. 4.4 - Laws of Logarithms

  11. More Examples – pg. 329 • Evaluate the expression. 4.4 - Laws of Logarithms

  12. More Examples – pg. 329 • Use the Law of Logarithms to expand the expression. 4.4 - Laws of Logarithms

  13. More Examples – pg. 329 • Use the Laws of Logarithms to combine the expression. 4.4 - Laws of Logarithms

  14. More Examples – pg. 330 • Use the Change of Base Formula and a calculator to evaluate the logarithm, rounded to 6 decimal places. Use either natural or common logarithms. 4.4 - Laws of Logarithms

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