3.2 Day 1
Exponential to Logarithmic Form
3.2 Day 1 Objectives Students will recognize and evaluate logarithmic functions with base a and base e
Students will graph logarithmic functions
Students will use technology to gain a better understanding of their mathematical modeling
1
Review
Decide whether each function is Power, Exponential, or Neither.
A. y= 2x
B. y= x2
2
C. y= 5
Exponential D. y= ex Exponential
Power E. y= e3 Neither
Neither
3.2 Log Functions and their Graphs
Since f(x)=ax is 1 to 1, it has an inverse called the logarithmic function with base a. To be 1 to 1 means that the graph passes both the
HORIZONTAL LINE TEST and VERTICAL LINE TEST
Log Function with base a
For x>0, a>0, and a=1: y=logax if and only if x=ay
f(x) = logax reads as "log x base a"
f(x) = logax is called the logarithmic function with base a
Log Form
Exponential Form
y=logax
2=log39
x=ay
9=32
log5125=3 53=125
log28=3
23=8
Log Form
1
log3 =­2
9
1
log497= 2
log61=0
Exponential Form
3­2= 19
1
2 49 =7
60=1
Evaluate each at the indicated value of x
1. log2x, x=8
2. log4x, x=2
8
= 3
3. log3x, x=1
100
1
2
= 4. log10x, x= 1
= 0
= ­2
TI­84 Help
Find log232
log 32
log 2
or
Log
2
= 5
32
= 5
alpha window 5
log base(
Properties of Logs
1)
2)
3)
4)
loga1 = 0
logaa = 1
logaax = x
a logax = x
5) if logax = logay
then x = y
Example:
x=5
3
= 5
Try these! 1. log443 =
2. logaa5
y=log x has base ___
10
e
y=ln x has base ___
10
10
3. logbb­2 = ­2
y=log x has base ___
y=ln x has base ___
Log Equation
Exponential Equation
4
Attachments
Pre Calc 3.2.notebook