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