1. WARMUP Lesson 7.5, For use with pages 507-513 Evaluate the logarithm.
Try not to use a calculator except to guess and check..
1. log5 625
ANSWER 4
2. log
ANSWER –5
ANSWER 1 5
3. log32 2
4. log36 1 6
ANSWER 1 2 – 2 3
5. log8 4
ANSWER

2. 7.5 Notes - Apply Properties of Logs

3. Properties of Exponents - REVIEW
Multiplication  Addition
Division  Subtraction
Exponent  Multiplication

4. Multiplication  Addition
Properties of Logarithms
Product Property
Multiplication  Addition
Quotient Property
Division  Subtraction
Power Property
Exponent  Multiplication
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5. 1) 2) 3)

6. 1) 2) 3)

11. Change-of-Base Formula

12. 1) 2)

13. 1) 2)

14. cooldown Lesson 7.5, For use with pages 507-513
Evaluate the logarithm.
Try not to use a calculator except to guess and check..
1. log5 625
ANSWER 4
2. log
ANSWER –5
ANSWER 1 5
3. log32 2
4. log36 1 6
ANSWER 1 2 – 2 3
5. log8 4
ANSWER

15. Use properties of logarithms
EXAMPLE 1
Use properties of logarithms 3 4
log
Use
0.792 and 7
1.404 to evaluate the
logarithm. a. 4
log 3 7 = 3 – 4
log 7
Quotient property
0.792
1.404 –
Use the given values of 3 4
log 7.
and =
–0.612
Simplify. b. 4
log 21 = 4
log
(3 7)
Write 21 as = 3 4
log + 7
Product property
0.792
1.404 +
Use the given values of 3 4
log 7.
and =
2.196
Simplify.

16. Use properties of logarithms
EXAMPLE 1
Use properties of logarithms 3 4
log
Use
0.792 and 7
1.404 to evaluate the
logarithm. c. 4
log 49 72 = 4
log
Write 49 as 72 4
log = 2 7
Power property
2(1.404)
Use the given value of 7. 4
log =
2.808
Simplify.

17. GUIDED PRACTICE
for Example 1 5 6
log
Use
0.898 and 8
1.161 to evaluate the
logarithm. 1. 5 8 6
log 6
log 3. 64
SOLUTION
SOLUTION
2.322
–0.263 4. 6
log
125 2. 6
log 40
SOLUTION
2.059
SOLUTION
2.694

18. Expand a logarithmic expression
EXAMPLE 2
Expand a logarithmic expression
Expand 6
log
5x3 y
SOLUTION 6
log
5x3 y =
5x3 y 6
log –
Quotient property = 5 6
log x3 y – +
Product property = 5 6
log x y – + 3
Power property

19. Standardized Test Practice
EXAMPLE 3
Standardized Test Practice
SOLUTION –
log 9 + 3log2
log 3 = –
log 9 + log 23
log 3
Power property =
log
( ) 23 –
log 3
Product property =
log 9 23 3
Quotient property = 24
log
Simplify.
The correct answer is D.
ANSWER

20. GUIDED PRACTICE
for Examples 2 and 3
Expand 5.
log 3 x4 .
SOLUTION
log log x
Condense ln ln 3 – ln 12. 6.
SOLUTION
ln 9

21. EXAMPLE 4
Use the change-of-base formula 3
log 8
Evaluate
using common logarithms and natural
logarithms.
SOLUTION
Using common logarithms: =
log 8
log 3
0.9031
0.4771 3
log 8
1.893
Using natural logarithms: =
ln 8
ln 3
2.0794
1.0986 3
log 8
1.893

22. EXAMPLE 5
Use properties of logarithms in real life
Sound Intensity
For a sound with intensity I (in watts per square meter), the loudness L(I) of the sound (in decibels) is given by the function =
log
L(I) 10 I I
where is the intensity of a barely audible sound (about watts per square meter). An artist in a recording studio turns up the volume of a track so that the sound’s intensity doubles. By how many decibels does the loudness increase?
10–12

23. Use properties of logarithms in real life
EXAMPLE 5
Use properties of logarithms in real life
SOLUTION
Let I be the original intensity, so that 2I is the doubled intensity.
Increase in loudness =
L(2I) – L(I)
Write an expression. =
log 10 I 2I –
Substitute. = 10
log – 2I I I
Distributive property = 2 10
log I – +
Product property 10
log 2 =
Simplify.
3.01
Use a calculator.
ANSWER
The loudness increases by about 3 decibels.

24. GUIDED PRACTICE
for Examples 4 and 5
Use the change-of-base formula to evaluate the logarithm. 5
log 8 7.
SOLUTION
about 8
log 14 8.
SOLUTION
about

25. GUIDED PRACTICE
for Examples 4 and 5
Use the change-of-base formula to evaluate the logarithm. 26
log 9 9.
SOLUTION
about
10. 12
log 30
SOLUTION
about

26. GUIDED PRACTICE
for Examples 4 and 5
WHAT IF? In Example 5, suppose the artist turns up the volume so that the sound’s intensity triples. By how many decibels does the loudness increase?
11.
SOLUTION
about decibels

27. 7.5 Assignment 7.5: 3-6 All, 7-59 ODD for 6/5 pts
OR 3-6 All, 7-59 EOO for 5/5 pts
Show Work.
DO NOT use your calculator until problem number 45.
Write down these hints:
Remember:
And, log 1 = 0 no matter what the base.
And, logbb = 1
And, ln x = loge x We call it a Natural Log.
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28. Daily Homework Quiz
For use after Lesson 7.5
For #1 & 2, Use log and log to evaluate the logarithm. NO CALCULATOR 
1. log5 160
ANSWER
3.153
2. log5 8000
ANSWER
5.583 3 y2
3. Expand ln .
ANSWER 1 3
ln 3 – 2 ln y
4. Condense 5 log2 x – 4 log2 y .
ANSWER
log2 y4 . x5
5. Use the change-of- base formula to evaluate log4 50. Calculator OK.
2.822
ANSWER
B. The intensity level of an electric guitar is watts per square meter. Use the formula L (I)=10 log where I –12 watts per square meter, to find the decibel level of the guitar. I I0
ANSWER
about 148 decibels