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Properties of Logarithms

Properties of Logarithms. Section 7.4. Review. Product: Quotient: Power:. n + m. n – m. n* m. Review. Review: What’s and Answer: 8 and 16 because its 2 · 2 · 2 = 8 and 2 · 2 · 2 · 2 = 16. So we know that and . However, what’s

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Properties of Logarithms

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  1. Properties of Logarithms Section 7.4 7.4 - Properties of Logarithms Honors

  2. Review • Product: • Quotient: • Power: n + m n – m n* m 7.4 - Properties of Logarithms Honors

  3. Review • Review: What’s and • Answer: 8 and 16 because its 2 · 2 · 2 = 8 and 2 · 2 · 2 · 2 = 16. • So we know that and . However, what’s We’ll answer that question later… 7.4 - Properties of Logarithms Honors

  4. Exponential and logarithmic operations undo each other since they are inverse operations.

  5. Example 1: Recognizing Inverses Simplify each expression. b. log381 c. 5log510 a. log3311 5log510 log3311 log334 10 11 4

  6. Example 2 a. Simplify log100.9 b. Simplify 2log2(8x) 2log2(8x) log 100.9 8x 0.9

  7. Properties of Logarithms • Product: • Quotient: • Power: 7.4 - Properties of Logarithms Honors

  8. Example 3: Adding Logarithms Express log64 + log69 as a single logarithm. Simplify. log64 + log69 log6 (4  9) log6 36 2

  9. Example 4 Simplify as a single logarithm. What is the operation shown in this problem? MULTIPLY/PRODUCT

  10. Example 5 simplify as a single logarithm. What is the operation shown in this problem? MULTIPLY/PRODUCT 7.4 - Properties of Logarithms Honors

  11. Example 6 Simplify as a single logarithm. What is the operation shown in this problem?DIVIDE/QUOTIENT

  12. Example 7 Simplify as a single logarithm. What is the operation shown in this problem? DIVIDE/QUOTIENT 7.4 - Properties of Logarithms Honors

  13. Example 8 Express as a single logarithm. Simplify, if possible. 2

  14. Example 9 Express as a single logarithm. Simplify, if possible. 1

  15. Example 10 simplify as a single logarithm. What is the operation shown in this problem? POWER PROPERTY 7.4 - Properties of Logarithms Honors

  16. Example 11 Simplify as a single logarithm. What is the operation shown in this problem? POWER PROPERTY 7.4 - Properties of Logarithms Honors

  17. Example 12 simplify as a single logarithm. 7.4 - Properties of Logarithms Honors

  18. Example 13 • Solve for x, 7.4 - Properties of Logarithms Honors

  19. Example 14 • Solve for x, 7.4 - Properties of Logarithms Honors

  20. Example 15 simplify as a single logarithm. 7.4 - Properties of Logarithms Honors

  21. Example16 simplify 7.4 - Properties of Logarithms Honors

  22. Your Turn • Simplify: • Simplify: • Simplify: • Simplify: 7.4 - Properties of Logarithms Honors

  23. Example 12 • The Richter magnitude of an earthquake, M, is related to the energy released in ergs, E, by the formula . . Find the energy released by an earthquake of magnitude 4.2. 7.4 - Properties of Logarithms Honors

  24. Assignment Pg 516: 20-35 all, omit 34 20-31 use without a graphing calculator 7.4 - Properties of Logarithms Honors

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