November 17, 2015
(3.3) Logarithmic Functions and Their Graphs
Objective: To learn about Inverses of Exponential Functions,
common logs, natural logs, and graphs of logs.
Why: Logarithmic functions are used in many applications,
including the measurement of the relative intensity of sounds.
November 17, 2015
y=bx
Obj: To learn about Inverses of Exponential Functions, common
logs, natural logs, and graphs of logs.
Is this a function?
Is it one-to-one?
What does that mean?
What does it's inverse look like?
What function type is the inverse?
y=bx
y = logbx
domain:
domain:
range:
range:
November 17, 2015
f(x) = log x
domain: ____________
range: _____________
continuity: ___________
symmetry: ___________
boundedness: ____________
asymptotes: _____________
extrema: ____________
end behavior using limits: ____________
November 17, 2015
November 17, 2015
Obj: To learn about Inverses of Exponential Functions, common
logs, natural logs, and graphs of logs.
Rewrite each statement to either exponential form or logarithmic
form.
1. log 100 = 2
3. 52 = 25
2. log3 81 = 4
4. 10-1 =
1
10
November 17, 2015
Obj: To learn about Inverses of Exponential Functions, common
logs, natural logs, and graphs of logs.
Evaluate.
1. log2 8
2. log3√3
3. log5
1
25
4. log4 1
5. log
6. ln
1
1000
1
e7
November 17, 2015
Basic Properties of Logarithms
logb 1 =
logb b =
logb by =
blogbx =
Obj: To learn about Inverses of Exponential Functions, common
logs, natural logs, and graphs of logs.
November 17, 2015
Evaluate.
Obj: To learn about Inverses of Exponential Functions, common
logs, natural logs, and graphs of logs.
1. log 100
4. ln √e
2. 10log6
5. eln(1/5)
3.
6. ln e5
6log611
November 17, 2015
Solve the equation.
1. log x = 4
Obj: To learn about Inverses of Exponential Functions, common
logs, natural logs, and graphs of logs.
2. log x = -3
November 17, 2015
Obj: To learn about Inverses of Exponential Functions, common
logs, natural logs, and graphs of logs.
Transformations:
f(x) = a log (bx - c) + d
Describe the transformations to y = ln x or y = log x.
1. g(x) = 3 log x
2. g(x) = ln (x + 3)
November 17, 2015
HW:
Obj: To learn about Inverses of Exponential Functions, common
logs, natural logs, and graphs of logs.
Day2: (3.3)Pg.281:2-24ev, 34, 36, 60, 62
HR: (3.3)Pg.281: 1-23odd, 37,39,41,47,51