Lesson 4 Menu Five-Minute Check (over Lesson 9-3) Main Ideas and Vocabulary Example 1: Find Common...
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Transcript of Lesson 4 Menu Five-Minute Check (over Lesson 9-3) Main Ideas and Vocabulary Example 1: Find Common...
![Page 1: Lesson 4 Menu Five-Minute Check (over Lesson 9-3) Main Ideas and Vocabulary Example 1: Find Common Logarithms Example 2: Real-World Example: Solve Logarithmic.](https://reader036.fdocuments.in/reader036/viewer/2022062417/55157ef3550346a1418b5576/html5/thumbnails/1.jpg)
Five-Minute Check (over Lesson 9-3)
Main Ideas and Vocabulary
Example 1: Find Common Logarithms
Example 2: Real-World Example: Solve Logarithmic Equations
Example 3: Solve Exponential Equations Using Logarithms
Example 4: Solve Exponential Inequalities Using Logarithms
Key Concept: Change of Base Formula
Example 5: Change of Base Formula
![Page 2: Lesson 4 Menu Five-Minute Check (over Lesson 9-3) Main Ideas and Vocabulary Example 1: Find Common Logarithms Example 2: Real-World Example: Solve Logarithmic.](https://reader036.fdocuments.in/reader036/viewer/2022062417/55157ef3550346a1418b5576/html5/thumbnails/2.jpg)
• common logarithm
• Change of Base Formula
• Solve exponential equations and inequalities using common logarithms.
• Evaluate logarithmic expressions using the Change of Base Formula.
![Page 3: Lesson 4 Menu Five-Minute Check (over Lesson 9-3) Main Ideas and Vocabulary Example 1: Find Common Logarithms Example 2: Real-World Example: Solve Logarithmic.](https://reader036.fdocuments.in/reader036/viewer/2022062417/55157ef3550346a1418b5576/html5/thumbnails/3.jpg)
Find Common Logarithms
A. Use a calculator to evaluate log 6 to four decimal places.
Answer: about 0.7782
Keystrokes: ENTERLOG 6 .7781512504
![Page 4: Lesson 4 Menu Five-Minute Check (over Lesson 9-3) Main Ideas and Vocabulary Example 1: Find Common Logarithms Example 2: Real-World Example: Solve Logarithmic.](https://reader036.fdocuments.in/reader036/viewer/2022062417/55157ef3550346a1418b5576/html5/thumbnails/4.jpg)
Find Common Logarithms
B. Use a calculator to evaluate log 0.35 to four decimal places.
Answer: about –0.4559
Keystrokes: ENTERLOG .35 –.4559319556
![Page 5: Lesson 4 Menu Five-Minute Check (over Lesson 9-3) Main Ideas and Vocabulary Example 1: Find Common Logarithms Example 2: Real-World Example: Solve Logarithmic.](https://reader036.fdocuments.in/reader036/viewer/2022062417/55157ef3550346a1418b5576/html5/thumbnails/5.jpg)
A. A
B. B
C. C
D. D
0% 0%0%0%
A. 0.3010
B. 0.6990
C. 5.0000
D. 100,000.0000
A. Which value is approximately equivalent to log 5?
![Page 6: Lesson 4 Menu Five-Minute Check (over Lesson 9-3) Main Ideas and Vocabulary Example 1: Find Common Logarithms Example 2: Real-World Example: Solve Logarithmic.](https://reader036.fdocuments.in/reader036/viewer/2022062417/55157ef3550346a1418b5576/html5/thumbnails/6.jpg)
A. A
B. B
C. C
D. D
0% 0%0%0%
A. –0.2076
B. 0.6200
C. 1.2076
D. 4.1687
B. Which value is approximately equivalent to log 0.62?
![Page 7: Lesson 4 Menu Five-Minute Check (over Lesson 9-3) Main Ideas and Vocabulary Example 1: Find Common Logarithms Example 2: Real-World Example: Solve Logarithmic.](https://reader036.fdocuments.in/reader036/viewer/2022062417/55157ef3550346a1418b5576/html5/thumbnails/7.jpg)
EARTHQUAKE The amount of energy E, in ergs, that an earthquake releases is related to its Richter scale magnitude M by the equation log E = 11.8 + 1.5M. The San Fernando Valley earthquake of 1994 measured 6.6 on the Richter scale. How much energy did this earthquake release?
log E = 11.8 + 1.5MWrite the
formula.
log E = 11.8 + 1.5(6.6)Replace M
with 6.6.
log E = 21.7 Simplify.
10log E = 1021.7 Write each side using 10 as a base.
Solve Logarithmic Equations
![Page 8: Lesson 4 Menu Five-Minute Check (over Lesson 9-3) Main Ideas and Vocabulary Example 1: Find Common Logarithms Example 2: Real-World Example: Solve Logarithmic.](https://reader036.fdocuments.in/reader036/viewer/2022062417/55157ef3550346a1418b5576/html5/thumbnails/8.jpg)
E= 1021.7
Inverse Property of Exponents and Logarithms
Answer: The amount of energy released was about 5.01 × 1021 ergs.
Solve Logarithmic Equations
E ≈ 5.01 × 1021
Use a calculator.
![Page 9: Lesson 4 Menu Five-Minute Check (over Lesson 9-3) Main Ideas and Vocabulary Example 1: Find Common Logarithms Example 2: Real-World Example: Solve Logarithmic.](https://reader036.fdocuments.in/reader036/viewer/2022062417/55157ef3550346a1418b5576/html5/thumbnails/9.jpg)
1. A
2. B
3. C
4. D
0%0%0%0%
A B C D
A. –7.29 ergs
B. –2.93 ergs
C. 22.9 ergs
D. 7.94 × 1022 ergs
EARTHQUAKE The amount of energy E, in ergs, that an earthquake releases is related to its Richter scale magnitude M by the equation log E = 11.8 + 1.5M. In 1999 an earthquake in Turkey measured 7.4 on the Richter scale. How much energy did this earthquake release?
![Page 10: Lesson 4 Menu Five-Minute Check (over Lesson 9-3) Main Ideas and Vocabulary Example 1: Find Common Logarithms Example 2: Real-World Example: Solve Logarithmic.](https://reader036.fdocuments.in/reader036/viewer/2022062417/55157ef3550346a1418b5576/html5/thumbnails/10.jpg)
Solve 5x = 62.
5x = 62 Original equation
log 5x = log 62Property of Equality for Logarithms
x log 5= log 62Power Property of Logarithms
Answer: 2.5643
Solve Exponential Equations Using Logarithms
Divide each side by log 5.
x ≈ 2.5643 Use a calculator.
![Page 11: Lesson 4 Menu Five-Minute Check (over Lesson 9-3) Main Ideas and Vocabulary Example 1: Find Common Logarithms Example 2: Real-World Example: Solve Logarithmic.](https://reader036.fdocuments.in/reader036/viewer/2022062417/55157ef3550346a1418b5576/html5/thumbnails/11.jpg)
Check You can check this answer by using a calculator or by using estimation. Since 52 = 25 and 53 = 125, the value of x is between 2 and 3. Thus, 2.5643 is a reasonable solution.
Solve Exponential Equations Using Logarithms
![Page 12: Lesson 4 Menu Five-Minute Check (over Lesson 9-3) Main Ideas and Vocabulary Example 1: Find Common Logarithms Example 2: Real-World Example: Solve Logarithmic.](https://reader036.fdocuments.in/reader036/viewer/2022062417/55157ef3550346a1418b5576/html5/thumbnails/12.jpg)
1. A
2. B
3. C
4. D
0%0%0%0%
A B C D
A. 0.3878
B. 2.5713
C. 2.5789
D. 5.6667
What is the solution to the equation 3x = 17?
![Page 13: Lesson 4 Menu Five-Minute Check (over Lesson 9-3) Main Ideas and Vocabulary Example 1: Find Common Logarithms Example 2: Real-World Example: Solve Logarithmic.](https://reader036.fdocuments.in/reader036/viewer/2022062417/55157ef3550346a1418b5576/html5/thumbnails/13.jpg)
Solve 27x > 35x – 3.27x
> 35x – 3
Original inequality log 27x
> log 35x – 3
Property of Inequality for Logarithmic Functions7x log 2
> (5x – 3) log 3
Power Property of Logarithms7x log 2
> 5x log 3 – 3 log 3
Distributive Property7x log 2 – 5x log 3
> – 3 log 3
Subtract 5x log 3 from each side.
Solve Exponential Inequalities Using Logarithms
![Page 14: Lesson 4 Menu Five-Minute Check (over Lesson 9-3) Main Ideas and Vocabulary Example 1: Find Common Logarithms Example 2: Real-World Example: Solve Logarithmic.](https://reader036.fdocuments.in/reader036/viewer/2022062417/55157ef3550346a1418b5576/html5/thumbnails/14.jpg)
x(7 log 2 – 5 log 3) > –3 log 3 Distributive Property
Solve Exponential Inequalities Using Logarithms
Divide each side by 7 log 2 – 5 log 3.
Switch > to < because 7 log 2 – 5 log 3 is negative.Use a calculator.
Simplify.
![Page 15: Lesson 4 Menu Five-Minute Check (over Lesson 9-3) Main Ideas and Vocabulary Example 1: Find Common Logarithms Example 2: Real-World Example: Solve Logarithmic.](https://reader036.fdocuments.in/reader036/viewer/2022062417/55157ef3550346a1418b5576/html5/thumbnails/15.jpg)
Check: Test x = 0.
27x > 35x – 3 Original inequality
Answer: The solution set is {x | x < 5.1415}.
Solve Exponential Inequalities Using Logarithms
?27(0)> 35(0) – 3 Replace x with 0.?20 > 3–3 Simplify.
Negative Exponent Property
![Page 16: Lesson 4 Menu Five-Minute Check (over Lesson 9-3) Main Ideas and Vocabulary Example 1: Find Common Logarithms Example 2: Real-World Example: Solve Logarithmic.](https://reader036.fdocuments.in/reader036/viewer/2022062417/55157ef3550346a1418b5576/html5/thumbnails/16.jpg)
A. A
B. B
C. C
D. D
0% 0%0%0%
A. {x | x > –1.8233}
B. {x | x < 0.9538}
C. {x | x > –0.9538}
D. {x | x < –1.8233}
What is the solution to 53x < 10x –2?
![Page 17: Lesson 4 Menu Five-Minute Check (over Lesson 9-3) Main Ideas and Vocabulary Example 1: Find Common Logarithms Example 2: Real-World Example: Solve Logarithmic.](https://reader036.fdocuments.in/reader036/viewer/2022062417/55157ef3550346a1418b5576/html5/thumbnails/17.jpg)
![Page 18: Lesson 4 Menu Five-Minute Check (over Lesson 9-3) Main Ideas and Vocabulary Example 1: Find Common Logarithms Example 2: Real-World Example: Solve Logarithmic.](https://reader036.fdocuments.in/reader036/viewer/2022062417/55157ef3550346a1418b5576/html5/thumbnails/18.jpg)
Express log3 18 in terms of common logarithms. Then approximate its value to four decimal places.
Answer: The value of log3 18 is approximately 2.6309.
Change of Base Formula
Use a calculator.
Change of Base Formula
![Page 19: Lesson 4 Menu Five-Minute Check (over Lesson 9-3) Main Ideas and Vocabulary Example 1: Find Common Logarithms Example 2: Real-World Example: Solve Logarithmic.](https://reader036.fdocuments.in/reader036/viewer/2022062417/55157ef3550346a1418b5576/html5/thumbnails/19.jpg)
A. A
B. B
C. C
D. D
0% 0%0%0%
What is log5 16 expressed in terms of common logarithms and approximated to four decimal places?
A.
B.
C.
D.
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