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