Lesson 5-6 Law of Logarithms

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:

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:

Express log b MN 2 in terms of log b M and log b N.

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!

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

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

Example:

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

Assignment: Pgs C.E.  #1 – 20 all W.E.  #1 – 20 all