Download presentation

Presentation is loading. Please wait.

Published byMadeline Clay Modified over 3 years ago

1
**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 Lesson 4 Menu

2
**Solve exponential equations and inequalities using common logarithms.**

Evaluate logarithmic expressions using the Change of Base Formula. common logarithm Change of Base Formula Lesson 4 MI/Vocab

3
**Find Common Logarithms**

A. Use a calculator to evaluate log 6 to four decimal places. Keystrokes: ENTER LOG 6 Answer: about Lesson 4 Ex1

4
**Find Common Logarithms**

B. Use a calculator to evaluate log 0.35 to four decimal places. Keystrokes: ENTER LOG .35 – Answer: about –0.4559 Lesson 4 Ex1

5
**A. Which value is approximately equivalent to log 5?**

B C D. 100, A B C D Lesson 4 CYP1

6
**B. Which value is approximately equivalent to log 0.62?**

D A B C D Lesson 4 CYP1

7
**Solve Logarithmic Equations**

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 = M. The San Fernando Valley earthquake of 1994 measured 6.6 on the Richter scale. How much energy did this earthquake release? log E = M Write the formula. log E = (6.6) Replace M with 6.6. log E = 21.7 Simplify. 10log E = Write each side using 10 as a base. Lesson 4 Ex2

8
**Solve Logarithmic Equations**

E = Inverse Property of Exponents and Logarithms E ≈ 5.01 × 1021 Use a calculator. Answer: The amount of energy released was about 5.01 × 1021 ergs. Lesson 4 Ex2

9
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 = M. In 1999 an earthquake in Turkey measured 7.4 on the Richter scale. How much energy did this earthquake release? A. –7.29 ergs B. –2.93 ergs C ergs D × 1022 ergs A B C D Lesson 4 CYP2

10
**Solve Exponential Equations Using Logarithms**

Solve 5x = 62. 5x = 62 Original equation log 5x = log 62 Property of Equality for Logarithms x log 5 = log 62 Power Property of Logarithms Divide each side by log 5. x ≈ Use a calculator. Answer: Lesson 4 Ex3

11
**Solve Exponential Equations Using Logarithms**

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, is a reasonable solution. Lesson 4 Ex3

12
**What is the solution to the equation 3x = 17?**

B C D A B C D Lesson 4 CYP3

13
**Solve Exponential Inequalities Using Logarithms**

Solve 27x > 35x – 3. 27x > 35x – 3 Original inequality log 27x > log 35x – 3 Property of Inequality for Logarithmic Functions 7x log 2 > (5x – 3) log 3 Power Property of Logarithms 7x log 2 > 5x log 3 – 3 log 3 Distributive Property 7x log 2 – 5x log 3 > – 3 log 3 Subtract 5x log 3 from each side. Lesson 4 Ex4

14
**Solve Exponential Inequalities Using Logarithms**

x(7 log 2 – 5 log 3) > –3 log 3 Distributive Property 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. Lesson 4 Ex4

15
**Solve Exponential Inequalities Using Logarithms**

Check: Test x = 0. 27x > 35x – 3 Original inequality ? 27(0) > 35(0) – 3 Replace x with 0. ? 20 > 3–3 Simplify. Negative Exponent Property Answer: The solution set is {x | x < }. Lesson 4 Ex4

16
**What is the solution to 53x < 10x –2?**

A. {x | x > –1.8233} B. {x | x < } C. {x | x > –0.9538} D. {x | x < –1.8233} A B C D Lesson 4 CYP4

17
Lesson 4 KC1

18
**Answer: The value of log3 18 is approximately 2.6309.**

Change of Base Formula Express log3 18 in terms of common logarithms. Then approximate its value to four decimal places. Change of Base Formula Use a calculator. Answer: The value of log3 18 is approximately Lesson 4 Ex5

19
**What is log5 16 expressed in terms of common logarithms and approximated to four decimal places?**

B. C. D. A B C D Lesson 4 CYP5

20
End of Lesson 4

Similar presentations

OK

Unit 5: Modeling with Exponential & Logarithmic Functions Ms. C. Taylor.

Unit 5: Modeling with Exponential & Logarithmic Functions Ms. C. Taylor.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on ancient indian mathematicians and their contributions Ppt on transportation in human beings what is the largest Convert word document to ppt online free Ppt on urinary catheter care Ppt on power transmission and distribution Ppt on sound navigation and ranging system of equations Ppt on tsunami the killer sea waves Convert pdf ppt to ppt online viewer Flat panel display ppt on tv Download ppt on nutrition in animals for class 7