7-5
Attributes of Logarithmic Functions
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SOLVE IT!
S
The chart shows the different ways you can write 4 and 16 in the form a b , where a
and b are positive integers and a ≠ 1. What is the smallest number you can write
in this a b form in four different ways? In five different ways? In seven different
ways? Explain how you found your answers.
Interactive
Exploration
Vocabulary
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Create Representations to Communicate Mathematical Ideas (1)(E)
Describe how the representation you made successfully organizes and
communicates your solution to the problem.
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Problem 1
P
Got It?
Writing Exponential Equations
in Logarithmic Form
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What is the logarithmic form of each equation?
8
ELPS
ELPS
EL
()
b. 27 = 23
a. 36 = 62
3
c. 1 = 30
Discuss with a classmate the new equation structure presented during classroom
instruction. Work together to write the logarithmic form of each equation in
the Got It. Listen to each other read the new equations, and help rephrase any
statements that do not use terms in the correct order.
TEKS Process Standard (1)(F)
Problem 2
P
Got It?
Evaluating a Logarithm
What is the value of each logarithm?
a. log 5 125
1
c. log 64 32
b. log 4 32
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TEKS Process Standard (1)(F)
Problem 3
P
Got It?
Graphing the Inverse of a Function
The volume of a cloud of gas increases by a factor of 10 every hour. The function
g (x) represents the volume of the cloud after x hours. Find g -1(x) and describe
what g -1(x) represents in this context.
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TEKS Process Standard (1)(D)
Problem 4
P
Got It?
Analyzing Attributes of Logarithmic Functions
Use the graphs of f (x) = log 2 x and g (x) = log 10 x in Problem 4 to determine
whether 7 , 6 , or = best completes each statement.
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a. f (0.5) ____ g (0.5)
b. f (1) _____ g (1)
c. f (5) _____ g (5)
Problem 5
P
Got It?
Finding the Maximum and Minimum of
Logarithmic Functions
Use the graphs of f (x) = log 2 x and g (x) = log 10 x to find the minimum and
maximum values of the functions on the interval [32, 100]. If necessary, round to
the nearest thousandth.
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Lesson Check
Do you know HOW?
1. Evaluate the logarithm log 2 14 . Use your answer to write an exponential
equation and its corresponding logarithmic equation.
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2. The minimum value of the function f (x) = log 2 x on an interval is 4. What is
the approximate minimum value of g (x) = log 10 x on the interval?
3. The function f (x) = log 2 x models the number of hours it takes for a single
cell to repeatedly divide into two until there are x cells. A test tube currently
contains 1024 cells. How long will it take until the test tube contains
8192 cells?
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Lesson Check
Do you UNDERSTAND?
4. Vocabulary Determine whether each logarithm is a common logarithm.
a. log 2 4
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b. log 64
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c. log 10 100
d. log 5 5
5. Connect Mathematical Ideas (1)(F) Explain how you could use the function
y = 6x to graph the logarithmic function y = log 6 x .
6. Create Representations to Communicate Mathematical Ideas (1)(E)
A student said that for all positive values of x, x 7 log x. Do you agree?
Use a graph to explain your answer.
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TEXAS Test Practice
T
Multiple Choice
For Exercises 1–4, choose the correct letter.
1. If log(4x) = 3, what is x?
A.
log 3
4
3
B. 4
C. 75
D. 1000
2. Which of the following is true about the graphs f (x) = log 2 (x) and
g (x) = log 10 (x)?
F. f (x) and g (x) intersect the x-axis at the same point.
G. g(x) 7 f (x) for all x.
H. f (x) and g (x) have different domains.
J. f (x) and g (x) have different ranges.
1
3. Which of the following is the logarithmic form of the equation 4-3 = 64
?
1
A. log -3 64
=4
1
C. log 4 64
= -3
1
B. log -3 4 = 64
D. log 1 4 = -3
64
4. What is the value of log 2 8?
F. 64
G. 8
H. 16
J. 3
Short Response
5. A single-celled bacterium divides every hour. The number N of bacteria after
t hours is given by the formula log 2 N = t.
a. After how many hours will there be 64 bacteria?
b. Explain in words or show work for how you determined the number
of hours.
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