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4.6 Apply Properties of Logarithms

4.6 Apply Properties of Logarithms. Properties of Logarithms. Let b, m, and n be positive numbers such that b is not equal to 1. Product Property: log b mn = log b m + log b n Quotient Property: log b = log b m – log b n Power Property : log b m n = n log b m. Example 1.

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4.6 Apply Properties of Logarithms

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  1. 4.6 Apply Properties of Logarithms

  2. Properties of Logarithms Let b, m, and n be positive numbers such that b is not equal to 1. Product Property: logbmn = logbm + logbn Quotient Property: logb = logbm – logbn Power Property : logbmn= n logbm

  3. Example 1 Use log35 = 1.465 and log36 = 1.631

  4. Example 2 Expand a logarithmic expression

  5. Example 3 Condense a logarithmic expression

  6. Guided Practice

  7. Guided Practice

  8. Change of Base Formula 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. Let x and c be positive numbers with c not equal to 1.

  9. Example 4 Evaluate log212 using common logarithms and natural logarithms. Common Logarithms Natural Logarithms

  10. Guided Practice Evaluate logarithms

  11. Homework Pg 157 #1-27

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