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Properties of Logarithms

Dive into the properties of logarithms, including product, quotient, and power rules. Learn how to simplify expressions and recognize inverse operations. Practice examples to enhance your understanding of logarithmic operations.

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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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