1. Extra 5 point pass if you can solve (and show how)…

2. 3.2 – Logarithmic Functions and Their Graphs

3. Some things to ponder…. What are the properties of exponential functions that we learned yesterday? Who remembers how to determine if a function has an inverse? Will an exponential function have an inverse?

4. y = a x has an inverse log a x=y y = a x is equivalent to log a y=x Remember that logs are exponents…. So log a x is the exponent to which “a” must be raised to obtain x

5. Ex. 1) log 2 8=? Ex. 2) log 2 32=? Ex 3) log 10 (1/100)=?

6. Log 47 74000=? 55 x =22500

7. Graphing Logs… y=log a x Domain : (0,∞) Range: (- ∞, ∞ ) x intercept: (1,0) increasing: (0, ∞)

8. Graph f(x)=log 2 x

9. Graph f(x)=log 3 x + 4

10. Transformations….. f(x)=log b x g(x)= alog b (c(x-h))+k The transformations are the same for “a”, “c”, “h”, and “k” for all the other functions we have studied….*absolute value, quadratic, exponential, etc.

11. Natural Log Function… f(x)=log e x lnx y=e x and y = lnx are inverses y=lnx implies e y =x

12. Properties… e 0 = e 1 = ln e x = e lnx = ln(1)= ln(0)= ln(-1)= If lnx = lny then

13. Simplify with out a calculator:

14. Day 1 - HW pg. 216 #’s 1 – 52 (3’s)

15. Bacteria in a bottle… There is a single bacterium in a bottle at 11:00pm, and it is a type that doubles once every minute. The bottle will be completely full of bacteria at 12:00 midnight – exactly one hour. In your opinion, what percentage of the bottle will be full when the bottle starts to look full? For what amount of time between 11:00 and 12:00 would they have plenty of room to grow and spread out? If you were a researcher in the lab, at what time between 11:00 and midnight might make you look in the bottle and think “I’d better get a bigger container for those bacteria!”?

16. Finding Domain of Ln Functions… f(x)=ln(x-2) *think about the properties of ln g(x)=ln(2-x) h(x)=lnx 2

17. Lets do the application (ex 10) on page 215 together… Graph #41 on page 216 Practice Problems to work on now pg. 216 #’s 20, 24, 26, 43, 47, 57, 59, 60, 61