1. 7.5a - Properties of Logarithms
Worksheet Key
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7.5a - Properties of Logarithms

2. 7.5a - Properties of Logarithms
Worksheet Key
12/7/2018 8:28 PM
7.5a - Properties of Logarithms

3. 7.5a - Properties of Logarithms
Worksheet Key
12/7/2018 8:28 PM
7.5a - Properties of Logarithms

4. 7.5a - Properties of Logarithms
Worksheet Key
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7.5a - Properties of Logarithms

5. 7.5a - Properties of Logarithms
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7.5a - Properties of Logarithms

6. Section 7.5A, Revised ©2013, vdang@houstonisd.org
NATURAL LOGARITHMS
Section 7.5A,
Revised ©2013,
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7.5a - Properties of Logarithms

7. 7.5a - Properties of Logarithms
Conversions
The base of Natural Log (ln) is e.
Convert: lne x = y to ey = x
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7.5a - Properties of Logarithms

8. 7.5a - Properties of Logarithms
Example 1
Convert ln 2/5 = –0.916 to exponential form
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7.5a - Properties of Logarithms

9. 7.5a - Properties of Logarithms
Your Turn
Convert ln 679 = to exponential form
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7.5a - Properties of Logarithms

10. 7.5a - Properties of Logarithms
Example 2
Convert e2 = to logarithmic form
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7.5a - Properties of Logarithms

11. 7.5a - Properties of Logarithms
Your Turn
Convert e2x = 3 to logarithmic form
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7.5a - Properties of Logarithms

12. Simplifying Natural Logarithms
The inverse of a natural base (e) is the natural log (ln)
If there is ln and e, they cancel each other out
Natural logarithms have the same properties as log base 10 and logarithms with other bases
The base of a natural log is e but it will never be written as the base.
ln + e = FELONY
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7.5a - Properties of Logarithms

13. Natural Logarithm Steps
ISOLATE the x
CONVERT by incorporating e as the base to both sides
Cancel any ln e ’s
Simplify using Natural Logarithm rules
Check
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7.5a - Properties of Logarithms

14. 7.5a - Properties of Logarithms
Example 3
Solve ln x = 4
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7.5a - Properties of Logarithms

15. 7.5a - Properties of Logarithms
Example 4
Solve ln x = 7
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7.5a - Properties of Logarithms

16. 7.5a - Properties of Logarithms
Your Turn
Solve 3 ln x – 6 = 9
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7.5a - Properties of Logarithms

17. Natural Logarithm Rules
Product:
Quotient:
Power:
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7.5a - Properties of Logarithms

18. 7.5a - Properties of Logarithms
Example 5
Expand ln 3x4
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7.5a - Properties of Logarithms

19. 7.5a - Properties of Logarithms
Your Turn
Condense (ln ln 3) – ln 12
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7.5a - Properties of Logarithms

20. 7.5a - Properties of Logarithms
Example 6
Solve ex + 5 = 60
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7.5a - Properties of Logarithms

21. 7.5a - Properties of Logarithms
Example 7
Solve –14 + 3ex = 11
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7.5a - Properties of Logarithms

22. 7.5a - Properties of Logarithms
Your Turn
Solve 7 – 2ex = 5
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7.5a - Properties of Logarithms

23. 7.5a - Properties of Logarithms
Review
Solve x2 – 3x + 2 = 0
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7.5a - Properties of Logarithms

24. 7.5a - Properties of Logarithms
Example 8
Solve e2x – 3ex + 2 = 0
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7.5a - Properties of Logarithms

25. 7.5a - Properties of Logarithms
Example 8
Solve e2x – 3ex + 2 = 0
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7.5a - Properties of Logarithms

26. 7.5a - Properties of Logarithms
Example 9
Solve e2x – 7ex + 12 = 0
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7.5a - Properties of Logarithms

27. 7.5a - Properties of Logarithms
Example 10
Solve 2e2x + 7ex – 4 = 0
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7.5a - Properties of Logarithms

28. 7.5a - Properties of Logarithms
Your Turn
Solve 6e2x + 11ex – 2 = 0
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7.5a - Properties of Logarithms

29. 7.5a - Properties of Logarithms
Assignment
Worksheet
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7.5a - Properties of Logarithms