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Section 7-5

Section 7-5. Properties of Logarithms. Objectives. I can evaluate Common Logs using a calculator I can use Change Base Rule I can expand log expressions using log properties I can condense log expressions using properties. Common Logarithms.

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Section 7-5

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  1. Section 7-5 Properties of Logarithms

  2. Objectives • I can evaluate Common Logs using a calculator • I can use Change Base Rule • I can expand log expressions using log properties • I can condense log expressions using properties

  3. Common Logarithms • Your calculator has a button in the 7th row called LOG. • This button will calculate the base 10 common logarithm of a number. • Example: log 125 • = 2.097 • ROUND to 3 decimal places

  4. Examples • log 135 • = 2.130

  5. Change of Base Formula

  6. Find: log8 77 .

  7. Find: log16 64 .

  8. 3 Main Properties • Product Property • Quotient Property • Power Property

  9. Product Property • logb mn = logb m + logb n • You can use this property from left to right or from right back to the left. • Left to Right (Expanding) • Right to Left (Condensing)

  10. Product Rule • log2 4x • = log2 4 + log2 x • This is called expanding a log expression

  11. Working Backwards • log3 x + log3 3 + log3 9 • log3 3x + log3 9 • log3 27x • This is called condensing an expression

  12. Quotient Property • logb m/n = logb m – logb n • Left to Right (Expanding) • Right to Left (Condensing)

  13. Quotient Rule This is Expanding

  14. Working Backwards • log3 x - log3 3 • log3 x/3 • This is called condensing an expression

  15. Power Property • logb mp = p logb m • Left to Right (Expanding) • Right to Left (Condensing)

  16. Power Rule • log2 x3 • = 3log2 x • This is Expanding

  17. Conversions

  18. Condensing

  19. Condensing

  20. Homework • Worksheet 11-4

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