Lesson 5-6 Law of Logarithms. Remember: Logs are inverses of exponentials.
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Lesson 5-6 Law of Logarithms
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Transcript of Lesson 5-6 Law of Logarithms. Remember: Logs are inverses of exponentials.
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: If M and N are positive real numbers and b is a positive number other than 1,
then:
Laws of Logarithms: If M and N are positive real numbers and b is a positive number other than 1,
then:
Laws of Logarithms: If M and N are positive real numbers and b is a positive number other than 1,
then:
Laws of Logarithms: If M and N are positive real numbers and b is a positive number other than 1,
then:
Laws of Logarithms: If M and N are positive real numbers and b is a positive number other than 1,
then:
Example:
Example: Express logbMN2 in terms of logbM and logbN.
Example: Express logbMN2 in terms of logbM and logbN.
1st: Recognize that you are taking the log of a product (M)(N2)So we can split that up as an addition of two separate logs!
Example: Express logbMN2 in terms of logbM and logbN.
1st: Recognize that you are taking the log of a product (M)(N2)So we can split that up as an addition of two separate logs!
Logb MN2 = logbM + logbN2
Example: Express logbMN2 in terms of logbM and logbN.
1st: Recognize that you are taking the log of 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
Example:
Example:
Example:
Example:
Example:
Example:
Example:
Example:
Example:
Now the domain of all log statements is (0, ∞) x ≠ - 2 so x = 4 is the only solution.
Assignment:
Pgs. 199-200C.E. #1 – 20 allW.E. #1 – 20 all
