1. PROPERTIES OF LOGARITHMS
Section 7.5,
Revised ©2013,
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7.5 - Properties of Logarithms

2. 7.5 - Properties of Logarithms
REVIEW EXPONENT RULES
A. Product:
B. Quotient:
C. Power:
n + m
n – m
n* m
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7.5 - Properties of Logarithms

3. 7.5 - Properties of Logarithms
Logarithm PROPERTIES
A. Product:
B. Quotient:
C. Power: + ÷
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7.5 - Properties of Logarithms

4. 7.5 - Properties of Logarithms
EXPAND VS CONDENSE
A. Expanding Logarithms involves breaking down a simpler component into a complicated expression. The answer will involve more than one logarithm.
B. Condensing Logarithms involves breaking down a complicated expression into simpler components. The answer will involve ONLY one logarithm.
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7.5 - Properties of Logarithms

5. 7.5 - Properties of Logarithms
Example 1
Expand log3(4∙5)
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7.5 - Properties of Logarithms

6. 7.5 - Properties of Logarithms
Example 2
Expand log 3x
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7.5 - Properties of Logarithms

7. 7.5 - Properties of Logarithms
YOUR TURN
Expand log4xy
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7.5 - Properties of Logarithms

8. 7.5 - Properties of Logarithms
Example 3
Expand
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7.5 - Properties of Logarithms

9. 7.5 - Properties of Logarithms
Example 4
Expand
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7.5 - Properties of Logarithms

10. 7.5 - Properties of Logarithms
EXAMPLE 5
Expand
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7.5 - Properties of Logarithms

11. 7.5 - Properties of Logarithms
YOUR TURN
Expand
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7.5 - Properties of Logarithms

12. 7.5 - Properties of Logarithms
Example 6
Condense log3x + log38
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7.5 - Properties of Logarithms

13. 7.5 - Properties of Logarithms
Example 7
Condense log536 – log54
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7.5 - Properties of Logarithms

14. 7.5 - Properties of Logarithms
YOUR TURN
Condense and simplify, log26 – log24
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7.5 - Properties of Logarithms

15. 7.5 - Properties of Logarithms
Example 8
Solve for x, log42 – log4x = log4(2/3)
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7.5 - Properties of Logarithms

16. 7.5 - Properties of Logarithms
Example 9
Solve
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7.5 - Properties of Logarithms

17. 7.5 - Properties of Logarithms
YOUR TURN
Solve for x, log316 = xlog32
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7.5 - Properties of Logarithms

18. 7.5 - Properties of Logarithms
Example 10
Condense and Simplify log5100 – 2log52
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7.5 - Properties of Logarithms

19. 7.5 - Properties of Logarithms
Example 11
Condense (1/2)log536 –(1/3)log58
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7.5 - Properties of Logarithms

20. 7.5 - Properties of Logarithms
YOUR TURN
Condense (3log4x – 2log4y) + 7log4z
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7.5 - Properties of Logarithms

21. 7.5 - Properties of Logarithms
Example 12
Using , approximate log 63
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7.5 - Properties of Logarithms

22. 7.5 - Properties of Logarithms
Example 13
Using , approximate log 9/7
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7.5 - Properties of Logarithms

23. 7.5 - Properties of Logarithms
Example 14
Using , approximate log 81
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7.5 - Properties of Logarithms

24. 7.5 - Properties of Logarithms
YOUR TURN
Using , approximate log 81/49
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7.5 - Properties of Logarithms

25. 7.5 - Properties of Logarithms
Example 15
The Richter magnitude of an earthquake, M, is related to the energy released in ergs, E, by the formula Find the energy released by an earthquake of magnitude 4.2.
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7.5 - Properties of Logarithms

26. 7.5 - Properties of Logarithms
Example 15
The Richter magnitude of an earthquake, M, is related to the energy released in ergs, E, by the formula Find the energy released by an earthquake of magnitude 4.2.
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7.5 - Properties of Logarithms

27. 7.5 - Properties of Logarithms
Your turn
The Richter magnitude of an earthquake, M, is related to the energy released in ergs, E, by the formula Find the energy released by an earthquake of magnitude 6.2.
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7.5 - Properties of Logarithms

28. 7.5 - Properties of Logarithms
ASSIGNMENT
Worksheet
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7.5 - Properties of Logarithms