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

Find the inverse of:

*10 minute limit!!!

3.2 – Logarithmic Functions and Their Graphs

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?

y = ax has an inverse logax=y

y = ax is equivalent to logay=x

Remember that logs are exponents…. So logax is the exponent to which “a” must be raised to obtain x

Ex. 1) log28=?

Ex. 2) log232=?

Ex 3) log10(1/100)=?

Log4774000=?

55x=22500

Graphing Logs…

y=logax Domain: (0,∞)

Range: (- ∞, ∞ )

x intercept: (1,0)

increasing: (0, ∞)

Graph f(x)=log2x

Graph f(x)=log3x + 4

Transformations…..f(x)=logbx g(x)= alogb(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.

Natural Log Function…

f(x)=logex lnx

y=ex and y = lnx are inverses

y=lnx implies ey=x

Properties…e0=e1=ln ex=elnx=ln(1)=ln(0)=ln(-1)=If lnx = lny then

Simplify with out a calculator:

(a) ln(b) e ln5

(c) (d) 2 lne

Day 1 - HW

pg. 216 #’s 1 – 52 (3’s)

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!”?

Finding Domain of Ln Functions…

f(x)=ln(x-2) *think about the properties of ln

g(x)=ln(2-x)

h(x)=lnx2

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