1. Lesson 5-6 Law of Logarithms

2. Remember:

3. Logs are inverses of exponentials.

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

5. Laws of Logarithms:

6. If M and N are positive real numbers and b is a positive number other than 1, then:

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

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

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

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

11. Example:

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

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!

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

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

16. Example:

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

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