# 8­4 Properties of Logarithms Objective:   Discover and use the properties of logarithms. 8­4 Properties of Logarithms 2011

```8&shy;4 Properties of Logarithms 2011
April 27, 2011
8&shy;4 Properties of Logarithms
Objective: Discover and use the properties of logarithms.
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8&shy;4 Properties of Logarithms 2011
April 27, 2011
Check Skills You'll Need
Simplify each expression.
1. log2 4 + log2 8 2. log3 9 &shy; log3 27
3. log2 16/log2 64
Evaluate each expression for x = 3.
4. x3 &shy; x
5. x5 x2
6. x6/x9
7. x3 + x2
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8&shy;4 Properties of Logarithms 2011
April 27, 2011
With your partner or group, complete the Properties of Logarithms Activity.
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8&shy;4 Properties of Logarithms 2011
April 27, 2011
Use a calculator to find each answer.
1. log3 + log5 = 5. log(3 5) = 2. log1 + log7 = 6. log(1 7) = 3. log2 + log4 = 7. log(2 4) = 4. log10 + log2 = 8. log(10 2) = ∎
∎
∎
∎
Explain the pattern.
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8&shy;4 Properties of Logarithms 2011
April 27, 2011
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8&shy;4 Properties of Logarithms 2011
April 27, 2011
From your activity, you should have discovered the following properties:
You can use the properties of logarithms to rewrite logarithmic expressions.
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8&shy;4 Properties of Logarithms 2011
April 27, 2011
Identifying the Properties of Logarithms
State the property or properties used to rewrite each expression:
a. log2 8 &shy; log2 4 = log2 2
b. logb x3y = 3 logb x + logb y
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8&shy;4 Properties of Logarithms 2011
April 27, 2011
Simplifying Logarithms
Write each logarithmic expression as a single logarithm.
a. log3 20 &shy; log3 4
b. 3 log2 x + log2 y
c. 3 log 2 + log 4 &shy; log 16
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8&shy;4 Properties of Logarithms 2011
April 27, 2011
Expanding Logarithms
Expand each logarithm.
x
a. log5 ( )
y
b. log 3r4
c. log2 7b
y 2
d. log ( )
3
e. log7 a3b4
f. log √3b 9
8&shy;4 Properties of Logarithms 2011
April 27, 2011
HOMEWORK
Practice 8&shy;4
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