# Lesson 5-6 Law of Logarithms. Remember: Logs are inverses of exponentials.

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### Transcript of Lesson 5-6 Law of Logarithms. Remember: Logs are inverses of exponentials.

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Lesson 5-6 Law of Logarithms Slide 2 Remember: Slide 3 Logs are inverses of exponentials. Slide 4 Remember: Logs are inverses of exponentials. Therefore, all the rules of exponents will also work for logs. Slide 5 Laws of Logarithms: Slide 6 If M and N are positive real numbers and b is a positive number other than 1, then: Slide 7 Laws of Logarithms: If M and N are positive real numbers and b is a positive number other than 1, then: Slide 8 Laws of Logarithms: If M and N are positive real numbers and b is a positive number other than 1, then: Slide 9 Laws of Logarithms: If M and N are positive real numbers and b is a positive number other than 1, then: Slide 10 Laws of Logarithms: If M and N are positive real numbers and b is a positive number other than 1, then: Slide 11 Example: Slide 12 Express log b MN 2 in terms of log b M and log b N. Slide 13 Example: Express log b MN 2 in terms of log b M and log b N. 1 st : Recognize that you are taking the log of a product (M)(N 2 ) So we can split that up as an addition of two separate logs! Slide 14 Example: Express log b MN 2 in terms of log b M and log b N. 1 st : Recognize that you are taking the log of a product (M)(N 2 ) So we can split that up as an addition of two separate logs! Log b MN 2 = log b M + log b N 2 Slide 15 Example: Express log b MN 2 in terms of log b M and log b N. 1 st : Recognize that you are taking the log of a product (M)(N 2 ) So we can split that up as an addition of two separate logs! Log b MN 2 = log b M + log b N 2 Now, recognize that we have a power on the number in the 2 nd log. = log b M + 2log b N Slide 16 Example: Slide 17 Slide 18 Slide 19 Slide 20 Slide 21 Slide 22 Slide 23 Slide 24 Now the domain of all log statements is (0, ) x - 2 so x = 4 is the only solution. Slide 25 Assignment: Pgs. 199-200 C.E. #1 20 all W.E. #1 20 all