1. Warmup Alg 2 22 Mar 2012

2. Agenda Don't forget about resources on mrwaddell.net Assignment from last class period Sect 7.5: Properties of logarithms

3. Go over assignment from last class period

4. Section 7.5: Properties of Logarithms

5. Vocabulary Exponentials Logarithm log x ln x Any equation of the form x=(b) y The opposite of an exponential equation y= log b x No base? It is automatically base 10! “ln” is a shortcut way to write log e said “log base e”

6. Property of Logs and Exponents One-to-One Property of Exponential Functions and logs If b x = b y, then x = y. If log b x = log b y, then x = y.

7. Exponents First – Page 330

8. Exponents First

9. Product Property log b (nm) == log b n + log b m

10. Quotient Property log b = n m = log b n – log b m

11. Power Property log b m p = THIS IS EASILY THE MOST IMPORTANT ONE! = p log b m

12. Inverse Properties (2 of them) log b b x = x

13. Practice Problems Write each expression as a single logarithm. Then simplify if possible. log 2 5 + log 2 7 log 2 (5∙7) problem product property log 2 (35) finished

14. Practice Problems Write each expression as a single logarithm. Then simplify if possible. Log 5 36x 3 Log 5 36 + Log 5 x 2 problem product property Log 5 36 + 2Log 5 x Power property

15. Practice Problems Write each expression as a single logarithm. Then simplify if possible. problem quotient property product property power property

16. Practice Problems Write each expression as a single logarithm. Then simplify if possible. log 4 8 + log 4 2 log 4 (16) problem product property log 4 (4∙4) Hmm, what exponent for 4 x =16 2 is the answer!

17. Practice Problems Write each expression as a single logarithm. Then simplify if possible. log 3 3 5 - log 5 125 5log 3 3 – log 5 (5∙5∙5) problem power prop & factoring Inverse prop 2 is the answer! 5 – log 5 (5∙5∙5) 5 – 3 How many 5’s are there again?

18. Assignment Chapter 7.5: 15-30, 33 – 42, Pick 10 from each section