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Lesson 5-6

Lesson 5-6. Law of Logarithms. Remember:. Remember:. Logs are inverses of exponentials. Remember:. Logs are inverses of exponentials. Therefore, all the rules of exponents will also work for logs. Laws of Logarithms:. Laws of Logarithms:.

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Lesson 5-6

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  1. Lesson 5-6 Law of Logarithms

  2. Remember:

  3. Remember: Logs are inversesof exponentials.

  4. Remember: Logs are inversesof exponentials. Therefore, all the rules of exponents will also work for logs.

  5. Laws of Logarithms:

  6. Laws of Logarithms: If M and N are positive real numbers and bis a positive number other than 1, then:

  7. Laws of Logarithms: If M and N are positive real numbers and bis a positive number other than 1, then:

  8. Laws of Logarithms: If M and N are positive real numbers and bis a positive number other than 1, then:

  9. Laws of Logarithms: If M and N are positive real numbers and bis a positive number other than 1, then:

  10. Laws of Logarithms: If M and N are positive real numbers and bis a positive number other than 1, then:

  11. Example:

  12. Example: Express logbMN2 in terms of logbM and logbN.

  13. Example: Express logbMN2 in terms of logbM and logbN. 1st: Recognize that you are taking the logof a product  (M)(N2) So we can split that up as an addition of two separate logs!

  14. Example: Express logbMN2 in terms of logbM and logbN. 1st: Recognize that you are taking the logof a product  (M)(N2) So we can split that up as an addition of two separate logs! Logb MN2 = logbM + logbN2

  15. Example: Express logbMN2 in terms of logbM and logbN. 1st: Recognize that you are taking the logof a product  (M)(N2) So we can split that up as an addition of two separate logs! Logb MN2 = logbM + logbN2 Now, recognize that we have a power on the number in the 2nd log. = logbM + 2logbN

  16. Example:

  17. Example:

  18. Example:

  19. Example:

  20. Example:

  21. Example:

  22. Example:

  23. Example:

  24. Example: Now the domain of all log statements is (0, ∞)  x ≠ - 2 so x = 4 is the only solution.

  25. Assignment:Pgs. 199-200C.E. #1 – 20 allW.E. #1 – 20 all

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