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Mastering Properties of Logarithmic Functions

Learn the properties of logarithms, change of base, graphing with base b, re-expressing data, and key applications. Understanding how to add, subtract, multiply logarithms and work with logarithms as exponents. Explore examples showcasing product rule, expanding, condensing, evaluating logarithms, and utilizing the change-of-base formula.

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Mastering Properties of Logarithmic Functions

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  1. 3.4 Demana, Waits, Foley, Kennedy Properties of Logarithmic Functions

  2. What you’ll learn about • Properties of Logarithms • Change of Base • Graphs of Logarithmic Functions with Base b • Re-expressing Data … and why The applications of logarithms are based on their many special properties, so learn them well.

  3. Adding Logarithms • Evaluate and rewrite as a single log expression log10 + log100 = _______ = log( ) log10 + log1000 =_______ = log( ) log10 + log10 = _______ = log( ) logA + logB = log( ) Why does this work?

  4. Subtracting Logarithms • Evaluate and rewrite as a single log expression log1000 - log10 = _______ = log( ) log100 - log10 =_______ = log( ) log10 – log.01 = _______ = log( ) logA - logB = log( ) Why does this work?

  5. Logarithms with exponents

  6. Properties of Logarithms

  7. Example: Proving the Product Rule for Logarithms

  8. Solution

  9. Example: Expanding the Logarithm of a Product

  10. Solution

  11. Example: Condensing a Logarithmic Expression

  12. Solution

  13. Example: Evaluating Logarithms by Changing the Base

  14. Solution

  15. Change-of-Base Formula for Logarithms

  16. Example: Transforming Logarithmic Graphs

  17. Solution

  18. Solution

  19. Solution

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