1.unit 10 lesson 4b 2.cahsee boot camp 3.assignment check
TRANSCRIPT
Tues, March 03, 2015today’s agenda in
Algebra 2
1. Unit 10 Lesson 4b2. CaHSEE Boot Camp3. Assignment Check
Unit 10 Lesson 4b:Logarithmic FunctionsCCSS LESSON GOALS
F-LE 4.1: Prove simple laws of logs. F-LE 4.2: Use the definition of logs to translate between logarithms in any base. F-LE 4.3: Understand and use the properties of logarithms to simplify logarithmic numeric expressions and to identify their approximate values.
How can the properties of logarithms simplify and evaluate logarithmic expressions?
ESLRs: Becoming Competent Learners and Complex Thinkers
Another Logarithmic Property
loglog
logb
nb
mm
n
1, 1
, , and represent positive numbers
b n
b m n
loglog
logn
mm
n ln
loglnn
mm
n
Change-of-Base
Example
Evaluate using the Change-of-Base Property.
4log 8
log8
log 4ln8
ln 4
0.90308998699
0.60205999133
1.5
2.0794415417
1.3862943611
1.5
2
2
log 8
log 4
3
2
1.5
Example
Evaluate using the Change-of-Base Property.
81log 27
log 27
log81ln 27
ln81
1 .431363765
1.908485019
0.75
3.295836866
4.394449155
0.75
3
3
log 27
log 81
3
4
0.75
Example
Evaluate using the Change-of-Base Property.
8log 0.25
log0.25
log8ln 0.25
ln8
0.602059991
0.903089987
0.667
1.38629361
2.079441542
0.667
2
2
14log
log 8
2 2
2
log 1 log 4
log 8
0 2
3
814log
2
30.667
Example
Evaluate using the Change-of-Base Property.6log 15
log15
log6ln15
ln 6
1.1760912591
0.77815125038
1.511
2.7080502011
1.7917594692
1.511
You Try
Rewrite using the Change-of-Base Rule.2log 5
log5 ln5 or
log 2 ln 2
You Try
Rewrite using the Change-of-Base Rule.
512log 1 1
2 2log ln or
log5 ln5
0 log 2 0 ln 2 or
log5 ln5
log 2 ln 2 or
log5 ln5
log1 log 2 ln1 ln 2 or
log5 ln5
You Try
Evaluate using the Change-of-Base Rule.5log 125
5
5
log 125
log 5
3
3
1
Example
The magnitude of an measures the amount of energy released at its source. The Richter scale is an exponential measure of earthquake magnitude. Each point on the scale represents 30 times as much energy as the previous point.
0 1 2 3 4 5 6 7 8 9
30E 230E E 330E 430E 530E 630E 730E 830E 930E
The Richter Scalemagnitude
energy released
+ 1
X 30
Example
An earthquake of magnitude 7.9 occurred in 2001 in Gujarat, India. It released 74,903 times as much energy as a quake in 1994 in Reading, Pennsylvania . Find the magnitude of the Pennsylvania earthquake.
7.93074,903
30x
E
E
7.974,903 30 x
30log 74,903 7.9 x
log74,9037.9
log30x
4.8747.9
1.477x
3.3 7.9 x 4.6x
Example
An earthquake of magnitude 7.9 occurred in 2001 in Gujarat, India. It released 74,903 times as much energy as a quake in 1994 in Reading, Pennsylvania . Find the magnitude of the Pennsylvania earthquake.
0 1 2 3 4 5 6 7 8 9
30E 230E E 330E 430E 530E 630E 730E 830E 930E
The Richter Scalemagnitude
energy released
India, 2001 7.9
PA, 19944.6
X 30 X 30 X 30 X 30
3.374,903 30
Today’s Assignment
p. 496: 30 – 66 m; 72, 80 p. 508: “Quiz 2” # 6
CaHSEEBoot Camp
Preparing for the High School Exit Exam
Day 29
2
What is the volume of a cylinder with a height of 11 feet and a radius of 3 feet? V r h
1
9 cubic feet
33 cubic feet
66 cubic feet
99 cubic feet
0:020:030:040:070:080:120:130:140:150:160:170:180:220:230:240:280:290:300:310:320:330:340:350:360:420:430:450:470:490:500:520:530:540:560:581:000:590:570:550:510:480:440:410:400:390:380:370:270:260:250:210:200:190:110:100:090:060:050:460:01
A rectangular garden is 9 feet wide by 22 feet long.What is the area of the garden?
2
230 ft
260 ft
2188 ft
2198 ft
0:020:030:040:070:080:120:130:140:150:160:170:180:220:230:240:280:290:300:310:320:330:340:350:360:420:430:450:470:490:500:520:530:540:560:581:000:590:570:550:510:480:440:410:400:390:380:370:270:260:250:210:200:190:110:100:090:060:050:460:01
Lauren's gym charges her $150 every 6 months.If she spends an additional $10 a month to meetwith a trainer, what is Lauren's yearly gym cost?
3
$160
$300
$420
$3000
0:020:030:040:070:080:120:130:140:150:160:170:180:220:230:240:280:290:300:310:320:330:340:350:360:420:430:450:470:490:500:520:530:540:560:581:000:590:570:550:510:480:440:410:400:390:380:370:270:260:250:210:200:190:110:100:090:060:050:460:01
4
As time passed, the measuredroom temperature decreased.
As time passed, the measuredroom temperature increased.
There is a positive correlation betweentime and measured room temperature.
There is neither a positive correlationnor a negative correlation betweentime and measured room temperature.
Which of the following conclusions can be made from the scatterplot?
0:020:030:040:070:080:120:130:140:150:160:170:180:220:230:240:280:290:300:310:320:330:340:350:360:420:430:450:470:490:500:520:530:540:560:581:000:590:570:550:510:480:440:410:400:390:380:370:270:260:250:210:200:190:110:100:090:060:050:460:01
Time is Up!Please, pass
your warm-up forward
1
23 11V
9 11
9 cubic feet
33 cubic feet
66 cubic feet
99 cubic feet
2
What is the volume of a cylinder with a height of 11 feet and a radius of 3 feet? V r h
2
9 22A 230 ft
260 ft
2188 ft
2198 ft
A rectangular garden is 9 feet wide by 22 feet long.What is the area of the garden?
3
150 150 10 12
300 120$160
$300
$420
$3000
Lauren's gym charges her $150 every 6 months.If she spends an additional $10 a month to meetwith a trainer, what is Lauren's yearly gym cost?
Assignment Check
p. 496: 14 – 20 e, 32 – 56 m, 74, 77 p. 508: “Quiz 2” # 5
14 16 18 20
32 36 40 44
48 52 56 74
77
6 6 8 3
log 4 5log x 6 6log 10 log 3 12 ln 3lnx y 3
4 log x
2log5x ln5x 695log 22logs f
1.4
2
1
logC
EC
2 2log 4 log 16
2 42 2log 2 log 2
6
2 4
23log 4
223log 2
6
3 2
34log 9
8
234log 3
4 2
3ln1 ln e
0 3 1
3
ln1 3ln e
0 3ln e
5log 4 log x
log 4 5log x
6 6log 10 log 3
12 3ln lnx y
12 ln 3lnx y
34log x
34 log x
2log log5x
2log5x
212ln 20 ln ln x
14ln 20 ln ln x
14ln 20 x
ln5x
6 615 1 15 2 252log log
6 61 12 252log 3 log
122
6 6125log 3 log
6 615log 9 log
615log 9
695log
22logs f
2
1
1.4 logC
EC
1.4
2
1
logC
EC
Graph each function and fill-in the properties.
4"Quiz 2 #5" logy x
domain range
x-intercept y-intercept
asymptote
decreasing/increasing
end behavior
x
y
1
2
3
1 2 3–1 4 5 6–1
–2
–3
–4
–5
7
0x
1,0 none
0x
increasing
asymptote
x-intercept y-intercept
decreasing/increasing
end behavior
as 0 x f x as x f x
4log 4
1
y
4log 16
2
y
Today’s Assignment
p. 496: 30 – 66 m; 72, 80 p. 508: “Quiz 2” # 6