1. Chapter 10.2 Logarithms and Logarithmic Functions Standard & Honors
Algebra II Mr. Gilbert
Chapter 10.2
Logarithms and Logarithmic Functions
Standard & Honors
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2. Agenda
Warm up
Decay project
Lesson
Homework
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3. Homework Review
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4. Communicate Effectively
Logarithm: the inverse of the exponential function y=bx is x=by and it is called the logarithm of x.
Logarithm of x: is usually written y=logb x
Logarithmic function: y=logb x, where b>0 and b1.
Common Usage
Sound scale: decibels
Earthquake scale: Richter scale.
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5. Example 1 Logarithmic to Exponential Form (2)
Example 2 Exponential to Logarithmic Form (2)
Example 3 Evaluate Logarithmic Expressions (2)
Example 4 Inverse Property of Exponents and Logarithms (2)
Example 5 Solve a Logarithmic Equation (2)
Example 6 Solve a Logarithmic Inequality (3)
Example 7 Solve Equations with Logarithms on Each Side (3)
Example 8 Solve Inequalities with Logarithms on Each Side (2)
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Lesson 2 Contents

6. Write in exponential form.
Answer:
Write in exponential form.
Answer:
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Example 2-1a

7. Write each equation in exponential form. a.b.
Answer:
Answer:
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Example 2-1c

8. Special Values If b>0 and b1 then the following is true:
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9. Special Equalities
Because and are inverses:
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10. Write in logarithmic form.
Answer:
Write in logarithmic form.
Answer:
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Example 2-2a

11. Write each equation in logarithmic form. a.b.
Answer:
Answer:
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Example 2-2c

12. Let the logarithm equal y.
Evaluate
Let the logarithm equal y.
Definition of logarithm
Property of Equality for Exponential Functions
Answer: So,
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Example 2-3a

13. Evaluate
Answer: 3
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Example 2-3b

14. Evaluate .
Answer:
Evaluate .
Answer:
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Example 2-4a

15. Evaluate each expression. a.b.
Answer: 3
Answer:
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Example 2-4c

16. Definition of logarithm
Solve
Original equation
Definition of logarithm
Power of a Power
Simplify.
Answer:
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Example 2-5a

17. Solve
Answer: 9
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Example 2-5b

18. Solve Check your solution.
Original inequality
Logarithmic to exponential inequality
Simplify.
Answer: The solution set is
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Example 2-6a

19. Check Try 64 to see if it satisfies the inequality.
Original inequality
Substitute 64 for x.
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Example 2-6b

20. Solve Check your solution.
Answer:
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Example 2-6c

21. Solve Check your solution.
Original equation
Property of Equality for Logarithmic Functions
Subtract 4x and add 3 to each side.
Factor.
Zero Product Property or
Solve each equation.
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Example 2-7a

22. Check Substitute each value into the original equation.
Substitute 3 for x.
Simplify.
Original equation
Substitute 1 for x.
Simplify.
Answer: The solutions are 3 and 1.
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Example 2-7b

23. Solve Check your solution.
Answer: The solutions are 3 and –2.
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Example 2-7c

24. Property of Inequality for Logarithmic Functions
Solve
Original inequality
Property of Inequality for Logarithmic Functions
Addition and Subtraction Properties of Inequalities
We must exclude all values of x such that or Thus the solution set is and This compound inequality simplifies to
Answer: The solution set is
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Example 2-8a

25. Solve
Answer:
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Example 2-8b

26. Homework - Honors See Syllabus 10.2
pp : (multiples of 3), 68-72
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27. Homework
See Syllabus 10.2
pp : 21-32, 39-44, (multiples of 3), 68-70
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