6.5 props of logs.notebook

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6.5 - Properties of Logarithms

Objective: TSW Apply the properties of logarithms.

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Properties of LogarithmsIf M, N, and b are positive numbers and b≠1, then

Product Property: log b MN = log b M + log b N

Quotient Property:log b M = log b M - log b N

N

Section 5.5 2

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Properties of Logarithms

Power Property: log b Mp = p log b M

Section 5.5 3

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Examples: Expand the following logarithms.

1.

2.

3.

Section 5.5 4

Hint for Expanding:

1. separate division

2. separate multiplication

3. move exponents to the front of each term

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Now, condense the following logarithms into one logarithm…Use the properties backwards.

Section 5.5 5

4.

Hint for Condensing:

1. move front numbers to exponents

2. positive terms stay on top

3. negative terms move to the bottom

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Section 5.5 6

5.  

6.5 props of logs.notebook

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February 05, 2015

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Properties of Logarithmsb is a positive number and b≠1

log b 1 = 0 since b0 = 1Example: log 7 1

log b b = 1 , since b1 = bExample: log 7 7

Section 5.5 7

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Properties of Logarithms

log b bx = x, since bx = bxExample: log 7 72

blogbx = x , since log b x is the exponent to which b is raised to get x

Example: 7log72 4log48

Section 5.5 8

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Examples: Simplify the following:

6. log 9 1 + log 2 8

7. log 8 83 - log 3 1/9

8. 6log64 + log 4 64

9. log 6 6 - log 9 1

9

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Solve for x.

Section 5.5 10

11.  

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pgs. 512-513 #’s 7-25(odds), 29-49(odds)