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Properties of Logarithms

Properties of Logarithms. Goes along with 4.6 ( Green Book) 4.4 Quiz: Tomorrow Logarithms Test: 1/21/10. Vocabulary. Because of the relationship between logarithms and exponents, the properties of exponents have corresponding properties involving logarithms. Properties. Product Property:.

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Properties of Logarithms

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  1. Properties of Logarithms Goes along with 4.6 (Green Book) 4.4 Quiz: Tomorrow Logarithms Test: 1/21/10

  2. Vocabulary • Because of the relationship between logarithms and exponents, the properties of exponents have corresponding properties involving logarithms.

  3. Properties • Product Property:

  4. Properties • Quotient Property:

  5. Properties • Power Property:

  6. Properties • Change of Base: • Logarithms with any base other than 10 or e can be written in terms of common or natural logarithms using the change of base formula.

  7. Properties of Logarithms Continued…4.6 (Green) No School: Monday Logarithms Test: 1/21/10 (Thursday)

  8. Example 1: • Use log35 = 1.465 and log36 = 1.631 to evaluate the logarithm. • log36/5 • log330 • log336

  9. Example 2: • Expand the logarithm • log83x/y • lnx5y2z

  10. Example 3: • Condense the logarithm (Write as one logarithm) • ln x + 3 ln y – 2 ln 4 • 8 log x + ½ log y

  11. Example 4: • Evaluate • log212 • log94

  12. Remember this: • Graph y = log2(x + 2) • Now we can use the change of base formula and use our calculators to graph!!! YAY! 

  13. Example 5: • Average student scores on a memory exam are modeled by the function f(t) = 100 – 12log(t + 1) where t is the time in months. • Use properties of logarithms to write the model in condensed form. • Find the average score after 3 months.

  14. Homework: • Pg. 157 ALL

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