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Properties of Logarithmic Functions Objective: Simplify and evaluate expressions involving logarithms.

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### Transcript of Properties of Logarithmic Functions Objective: Simplify and evaluate expressions involving... Properties of Logarithmic Functions

Objective: Simplify and evaluate expressions involving logarithms.  7z 12t 3c 7z 12t 3c

3

3

nm

66ba 48sr Product and Quotient Properties of Logarithms

• For

• Product Property

:1,0,0,0 bbnm

nmmn bbb loglog)(log Product and Quotient Properties of Logarithms

• For

• Product Property

• Quotient Property

:1,0,0,0 bbnm

nmmn bbb loglog)(log

nm bbnm

b logloglog Product and Quotient Properties of Logarithms

• For

• Product Property

• Quotient Property

• You can use these properties to evaluate logarithmic expressions.

:1,0,0,0 bbnm

nmmn bbb loglog)(log

nm bbnm

b logloglog Example 1 Example 1 Example 1 Try This

• Given that , approximate each expression.

585.13log2

18log2 43

2log Try This

• Given that , approximate each expression.

585.13log2

18log2 43

2log

170.4585.1585.11

3log3log2log

332log

222

2 Try This

• Given that , approximate each expression.

585.13log2

18log2 43

2log

170.4585.1585.11

3log3log2log

332log

222

2

415.2585.1

4log3log 22 Example 2 Example 2 Example 2 Try This

• Write each expression as a single logarithm. Then, simplify if possible.

6log18log 44 yyx bb log3log4log 3 Try This

• Write each expression as a single logarithm. Then, simplify if possible.

6log18log 44 yyx bb log3log4log 3

3loglog 4618

4 Try This

• Write each expression as a single logarithm. Then, simplify if possible.

6log18log 44 yyx bbb log3log4log

3loglog 4618

4 34

34 loglog x

byyx

b The Power Property of Logarithms

• For , and any real number p:1,0,0,0 bbnm

mpm bp

b loglog Example 3 Example 3 Try This

• Evaluate .1003 27log Try This

• Evaluate .1003 27log

300310027log10027log 3100

3 Exponential-Logarithmic Inverse Properties

• For b > 0 and : 1b

0for log xxb xb

0for log xxb xb Example 4 Example 4 Example 4 Try This

• Evaluate each expression.

81log7 311log7 8log5

8338log Try This

• Evaluate each expression.

81log7 311log7 8log5

8338log

7411 Try This

• Evaluate each expression.

81log7 311log7 8log5

8338log

7411 1385 One-to-One Property of Logarithms

• If , then x = y.yx bb loglog Example 5 Example 5 Example 5  Homework

• Page 382• 13-61 odd