6.5 props of logs.notebook
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February 05, 2015
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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
Feb 58:37 AM Feb 56:51 AM
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)