1. Chapter 10.4 Common Logarithms Standard & Honors
Algebra II Mr. Gilbert
Chapter 10.4
Common Logarithms
Standard & Honors
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2. Agenda Warm up Work book (participation grade) Lesson Homework
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3. Homework Review
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4. Communicate Effectively
pH level: hydrogen ion h+ concentration
1.0 battery acid, Tomatoes, Black Coffee
7.0 Pure Water
7.8 Eggs, Milk of Magnesia, 13.5 Lye
pH Formula
Erg: measure of energy and mechanical work, the force required to accelerate a mass of one gram at a rate of one centimeter per second squared.
Richter Magnitude Formula
M = 2/3 log10 E | E seismic energy in 10,000,000 ergs.
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5. Examples: Richter Magnitude Scale (do not copy)
Breaking a rock on a lab table
1.0 Large Blast at a Construction Site
2.0 Large Quarry or Mine Blast
4.0 Small Nuclear Weapon
4.5 Average Tornado (total energy)
6.0 Double Spring Flat, NV Quake, 1994
7.0 Largest Thermonuclear Weapon
8.0 San Francisco, CA Quake, 1906
9.0 Chilean Quake, 1960
(San-Andreas type fault circling Earth)
(Fault Earth in half through center)
Source:
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6. Example 1 Find Common Logarithms (2)
Example 2 Solve Logarithmic Equations Using Exponentiation (3)
Example 3 Solve Exponential Equations Using Logarithms (2)
Example 4 Solve Exponential Inequalities Using Logarithms (3)
Example 5 Change of Base Formula (2)
Formula
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7. Use a calculator to evaluate log 6 to four decimal places.
ENTER
LOG
Keystrokes: 6
Answer: about
Use a calculator to evaluate log 0.35 to four decimal places.
ENTER
LOG
Keystrokes:
0.35 –
Answer: about –0.4559
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Example 4-1a

8. Use a calculator to evaluate each expression to four decimal places.
a. log 5
b. log 0.62
Answer:
Answer: –0.2076
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Example 4-1c

9. Write each side using 10 as a base.
Earthquake The amount of energy E, in ergs, that an earthquake releases is related to its Richter scale magnitude M by the equation log The San Fernando Valley earthquake of 1994 measured 6.6 on the Richter scale. How much energy did this earthquake release?
Write the formula.
Replace M with 6.6.
Simplify.
Write each side using 10 as a base.
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Example 4-2a

10. Inverse Property of Exponents and Logarithms
Use a calculator.
Answer: The amount of energy released was about ergs.
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Example 4-2b

11. Earthquake The amount of energy E, in ergs, that an earthquake releases is related to its Richter scale magnitude M by the equation log In 1999 an earthquake in Turkey measured 7.4 on the Richter scale. How much energy did this earthquake release?
Answer: about
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Example 4-2c

12. Property of Equality for Logarithmic Functions
Solve
Original equation
Property of Equality for Logarithmic Functions
Power Property of Logarithms
Divide each side by log 62.
Use a calculator.
Answer:
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Example 4-3a

13. Check You can check this answer by using a calculator or by using estimation. Since and the value of x is between 2 and 3. Thus, is a reasonable solution.
Solve
Answer:
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Example 4-3c

14. Solve Original inequality
Property of Inequality for Logarithmic Functions
Power Property of Logarithms
Distributive Property
Subtract 5x log 3 from each side.
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Example 4-4a

15. Use a calculator. Simplify. Distributive Property Divide each side by
Switch > to < because is negative.
Use a calculator.
Simplify.
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Example 4-4b

16. Negative Exponent Property
Check:
Original inequality
Replace x with 0.
Simplify.
Negative Exponent Property
Answer: The solution set is
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Example 4-4d

17. Solve
Answer:
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Example 4-4e

18. Answer: The value of is approximately 2.6309.
Express in terms of common logarithms. Then approximate its value to four decimal places.
Change of Base Formula
Use a calculator.
Answer: The value of is approximately
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Example 4-5a

19. Express. in terms of common logarithms
Express in terms of common logarithms. Then approximate its value to four decimal places.
Answer:
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Example 4-5b

20. Homework
See Syllabus 10.4
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