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Mastering Properties of Logarithms for Exponential Equations

Enhance your skills in solving exponential equations with logs by learning the Product, Quotient, and Power properties of logarithms. Follow simple steps for condensing and expanding expressions, and practice through helpful examples.

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Mastering Properties of Logarithms for Exponential Equations

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  1. Warm-Up April 14th

  2. HW Check HW 6.5 • a. 12,000 bacteria b. 96,000 bacteria c. 768,000 bacteria 2. 0.5 g • a. 6,800 insects b. 425 insects 4. 15 hours 5. 72 billion • a. 37,402,600 bact. b. 6,553,790 bact. 7. 2,609,610 people • a. 28.6 million b. 29.1 million • a. 689 bacteria b. 2986 bacteria • a. 172,800 termites b. 371,806 termites c. 627 termites

  3. Properties of Logarithms 6.6

  4. You’ve gotten good at solving exponential equations with logs… … but how would you handle something like this?

  5. Properties of Logarithms • Product Property • Quotient Property • Power Property The log bases must be the same in order to apply these properties!

  6. Product Property

  7. Quotient Property

  8. Power Property

  9. Steps for Condensing Step 1: Put everything in the sky (create exponents). Step 2: Combine.

  10. Example 1: Condense the following logarithmic expression.

  11. Example 2: Condense the following logarithmic expression.

  12. Example 3: Condense the following logarithmic expressions.

  13. Steps for Expanding Step 1: Separate the combinations. Step 2: Get everything out of the sky.

  14. Example 4: Expand the following logarithmic expression.

  15. Example 5: Condense the following logarithmic expression.

  16. Example 6: Condense the following logarithmic expressions.

  17. Quick Recap! To combine: • Put everything in the sky. • Combine. To expand: • Separate the combinations. • Get everything out the sky.

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