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Name: A2.L8-4.WU Date: Period:
THINK, PAIR, SHARE
Introduction to Logarithms
1. Look at the slip of paper you have received. 2. For each equation in exponential form, label the ππππ (π©), ππππππππ (π) and ππππ πππ(πΏ). (If youβre paper has logarithmic form do not do this step.) 3. Find the person in the room who has a slip of paper with the same numbers as you. (Their numbers can be physically smaller or be in a different position from yours, but the value must be the same.) 4. Assuming the base, exponent, and product have not changed, label each in the logarithmic equation on your partnerβs slip of paper. 5. Use the words base, exponent, and product to explain what you think a βlogβ is or does.
WARM-UP
Exponent Properties
Use your knowledge of exponent properties to answer the following questions.
π1
2 = βπ2 π1
3 = βπ3 πβπ =1
ππ
1. Which of the following is the expression below in simplest form?
(π2πβ3)β1
A. πβ2π3 B. π2π3
C. π2
π3
D. π3
π2
2. Which of the following is equivalent to the expression below?
6412
A. 4 B. 8 C. 32 D. 128
A2.L8-4.Notes
LESSON 8-4: LOGARITHMIC FUNCTIONS AS INVERSES Algebra Objective Students will be able to graph logarithmic functions and evaluate logarithmic
expressions. Language Objective Students will describe the process of evaluating a logarithm and justify their
choice to express a number as a particular power of a common base.
Big Idea
An exponential function of the form π¦ = ππ₯ has an inverse of the form π₯ = ππ¦ . To express βπ¦ ππ π ππ’πππ‘πππ ππ π₯β for the inverse, we write π¦ = logπ π₯.
You can read logπ π₯ as βπππ πππ π π ππ π₯.β In other words, the logarithm y is the exponent to which
be must be raised to get x.
π = πππππ (Logarithmic Form) π = ππ (Exponential Form)
If the logarithm does not have a base, we assume that the base is _______________.
Directions: Draw a line from each logarithm equation to its exponential equation in Column B.
Column A Column B 1. πππ2 16 = 4 A. 103 = 1000
2. πππ3 9 = 2 B. ππ¦ = π₯
3. πππ 1000 = 3 C. 32 = 9
4. ππππ π₯ = π¦ D. 24 = 16
Write each equation in exponential form. Use mental math to solve each equation.
5. π¦ = πππ3 27
6. π¦ = πππ5 25
A2.L8-4.Notes
Example #1
Evaluate πππ2 64
πππ2 64 = π₯
First, write in exponential form.
2π₯ = 64
Then, find a common base.
2π₯ = 26
Solve for the missing exponent.
2π₯ = 26
π₯ = 6
β΄ πππ2 64 = π
Check:
26 = 2 β 2 β 2 β 2 β 2 β 2 = 64
Example #2
Evaluate πππ3 81
Example #3
Evaluate πππ4 32
Example #4
Evaluate πππ8 16
Example #5
Evaluate πππ10 0.01
Example #6
Evaluate πππ2 0.5
A2.L8-4.Notes
Investigation 10-4: Graphs of Logarithmic Functions
Directions: Fill in the table below using your knowledge of logarithms and exponential functions. Then plot the points on the graph provided. Do you notice any symmetry between the graphs?
π¦ = πππ2π₯
π¦ = 2π₯
π₯ π¦
π₯ π¦
1
8 β3
1
4 β2
1
2 β1
1 0
2 1
2
3
4
A2.L8-4.Notes
CLASSWORK 10-4
Evaluating Logarithms
Evaluate each logarithm. (Complete #1-3, and at least 2 more problems for credit.)
1. log4 64
2. log5 625
3. log11 121
4. log10 0.1
5. log31
9
6. log2 0.25
7. log48 8. log927 9. log1664
Due by the end of class.
Name: A2.L10-4.HW
HOMEWORK 10-4
Logarithms and Logarithmic Functions
Directions: Write each equation in logarithmic form.
1. 92 = 81 2.
1
64= (
1
4)
3
3. 83 = 512
4. (1
3)
β2
= 9
5. 29 = 512 6. 45 = 1024 7. 54 = 625 8. 10β3 = 0.001
Directions: Evaluate each logarithm.
9. log2 128 10. log 100,000
11. log2(β32) 12. log7 76
13. log9 27 14. log4 32
15. log31
81
16. log1
3
1
9