1. Warmup Alg 2 16 Feb 2012

2. Warmup Alg 2 17 & 21 Feb 2012

3. Agenda Don't forget about resources on mrwaddell.net Sec 7.4: Intro to logarithms Definition of logs Inverses of logs

4. Go over assignment from last class period

5. Section 7.4: Introduction to Logarithms

6. Vocabulary Exponentials Logarithm Any equation of the form y=(b) x The opposite of an exponential equation y=b x if and only if Log b y=x

7. A different look BASE EXPONENT = POWER (exponential) 4 2 = 16 4 is the base. 2 is the exponent. 16 is the power. As a logarithm, log BASE POWER=EXPONENT log 4 16 = 2

8. A different way of saying the same thing. y= log b x is the inverse of x = b y, where b  1 and b > 0.

9. Examples Write the following in log or exponential form: 2 7 = 128 log 6 1296 = 4 3= log 7 343 3 5 = 243 log 2 128 = 7 6 4 = 1296 7 3 = 343 log 3 243 = 5

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

11. Inverse Properties (2 of them) log b b x = x log 2 2 8 = 8 5

12. Finding Inverses of functions y=log 7 x Using the definition of an inverse, becomes: y=7 x Switch the x and y’s, solve for y x=log 7 y Bcs of the def. of log & exponents

13. Finding Inverses of functions y=3 x Using the definition of an inverse, becomes: y=log 3 x Switch the x and y’s, solve for y x=3 y Bcs of the def. of log & exponents

14. Assignment Chapter 7.4: pg 503: 8-19, 28-33, 37-41

15. Graphing Log equations

16. Graphing Graph the function and state the domain, range and asymptote y= log 3 x Always crosses there (if not moved) 3 2 = 9 Domain: x > 0 Range: y is all real numbers Asymptote: x = 0

17. Graphing Graph the function and state the domain, range and asymptote y= log 1/2 x Always crosses there (if not moved) 2 2 = 4 Domain: x > 0 Range: y is all real numbers Asymptote: x = 0 2 3 = 8

18. Graphing Graph the function and state the domain, range and asymptote y= log 2 x

19. Graphing Graph the function and state the domain, range and asymptote y= log 5 x +2