Larson, Precalculus Functions and Graphs: A Graphing Approach, 5e Chapter 3
1. Graph the following function by hand; think of the transformations from the parent.
Learning Objective: Identify graph of exponential function
Section: 3.1
2.
Rewrite the logarithmic equation log 4
A)
416  – 2
B)
41/16  – 2
C)
4 –2 
1
 – 2 in exponential form.
16
–2
D)
1
  4
 16 
E)
1
4 –2  
16
1
16
Learning Objective: Write logarithmic equation in exponential form
Section: 3.2
3. Write the logarithmic equation below in exponential form.
ln 3 e 
1
3
1
1 3
e
3
e
 3 e C)  3 e D) e3  3 e E) e –3  3 e

e
B)
3
e
3
Learning Objective: Write logarithmic equation in exponential form
Section: 3.2
A)
4.
1
Rewrite the exponential equation 3–2  in logarithmic form.
9
A)
D)
1
log9 3  – 2
log3  – 2
9
B)
E)
1
log 2 9  – 2
log3  2
9
C)
log3 9  – 2
Learning Objective: Write exponential equation in logarithmic form
Section: 3.2
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Larson, Precalculus Functions and Graphs: A Graphing Approach, 5e Chapter 3
5.
Evaluate the function f ( x)  log 2 x at x 
A) 0
B) –1
C) –2
D) 2
E)
1
without using a calculator.
2
1
2
Ans: B
Learning Objective: Evaluate logarithmic function
Section: 3.2
6. Identify the x-intercept of the function y  3  log 2 x .
1
A) 8 B)
C) –3 D) 6 E) The function has no x-intercept.
8
Learning Objective: Identify x-intercept of logarithmic function
Section: 3.2
7. Identify the vertical asymptote of the function f ( x)  3  log( x  2) .
A)
x0
B)
x  –3
C)
x  2
D)
x2
E) The function has no vertical asymptote.
Learning Objective: Identify vertical asymptote of logarithmic function
Section: 3.2
8. Find the domain of the function below.
A)
B)
C)
 , –1
 , –3
 –3,  
 x +3
f  x   ln 

 x +1 
D)
 –1,  
E)
 , –3   –1, 
Learning Objective: Solve for the domain of a natural logarithmic function
Section: 3.2
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Larson, Precalculus Functions and Graphs: A Graphing Approach, 5e Chapter 3
9. Evaluate the logarithm log7 798 using the change of base formula. Round to 3 decimal
places.
A) 6.682 B) 0.291 C) 3.434 D) 13.003 E) 2.902
Learning Objective: Evaluate logarithm using change of base formula
Section: 3.3
10.
3
 1 
Simplify the expression log3   .
 27 
A) 3 B) –9 C) 0 D) –81 E) The expression cannot be simplified.
Ans: B
Learning Objective: Simplify a logarithmic expression
Section: 3.3
11. Use the properties of logarithms to expand the expression as a sum, difference, and/or
constant multiple of logarithms. (Assume all variables are positive.)
A)
B)
12log5 xyz
5log5 x + 4log5 y + 3log5 z
log 5 x 5 y 4 z 3
D)
log5 x  log5 y  log5 z +12
E)
log5 x  log5 y  log5 z + 60
C)
60log5 xyz
Learning Objective: Expand logarithm into sum, difference, and/or constant multiple of
logarithms
Section: 3.3
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Larson, Precalculus Functions and Graphs: A Graphing Approach, 5e Chapter 3
12. Use the properties of logarithms to expand the expression as a sum, difference, and/or
constant multiple of logarithms. (Assume all variables are positive.)
log b
A)
x y3
z6
D)
log b x + 3log b y
log b x + 6 log b y
6 log b z
12 log b z
B)
E)
log b x + 6 log b y
log b x + 3log b y
6 log b z
12 log b z
C)
1
logb x + 3logb y – 6 log b z
2
Learning Objective: Expand logarithm into sum, difference, and/or constant multiple of
logarithms
Section: 3.3
13. Condense the expression below to the logarithm of a single quantity.
4 ln x + 6 ln y – 4 ln z
D)
ln  x 4  y 6  z 4 
  xy 96 
ln    
 z  


4 6
B)
E)
x4  y6
x y
ln
ln 4
z4
z
C)
6 xy
ln
z
Learning Objective: Condense logarithmic expression using the properties of logs
Section: 3.3
A)
14. Find the exact value of log 4 28  log 4 7 without using a calculator.
1
7
A)
B) 1 C) 7 D)
E) 4
2
2
Learning Objective: Evaluate logarithmic function using properties of logarithms
Section: 3.3
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Larson, Precalculus Functions and Graphs: A Graphing Approach, 5e Chapter 3
15. Solve the equation f  x   g  x  algebraically.
f  x   ln e2 x+2
g  x   3x – 3
A) 2 B) –1 C) 5 D) –4 E) 1
Learning Objective: Solve logarithmic equation
Section: 3.4
16. Solve the logarithmic equation below.
ln  6 x – 6   2
e –2 + 6
e –2 – 6
e2 + 6
e2 – 6
B)
C)
D)
6
6
6
6
Ans: A
Learning Objective: Solve logarithmic equation
Section: 3.4
A)
E) 6e –2 + 36
17. Solve for x: 4 x / 3  0.0052 . Round to 3 decimal places.
A) 11.381 B) 15.777 C) 19.936 D) –19.936 E) –3.794
Learning Objective: Solve exponential equation
Section: 3.4
18. Solve the exponential equation below algebraically. Round your result to three decimal
places.
5t
0.707 

18 
  36
16 

A) 4.842 B) 2.622 C) 0.248 D) –2.523 E) –0.057
Learning Objective: Solve exponential equation
Section: 3.4
19. Solve the exponential equation below algebraically. Round your result to three decimal
places.
600e –6 x  90
A) 2.779 B) 0.316 C) –0.767 D) 0.064 E) –1.874
Learning Objective: Solve exponential equation
Section: 3.4
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Larson, Precalculus Functions and Graphs: A Graphing Approach, 5e Chapter 3
20. Solve the exponential equation below algebraically. Round your result to three decimal
places.
160e0.025 x  165, 000
A) 290.375 B) 275.774 C) 257.495 D) 277.541
Learning Objective: Solve exponential equation
Section: 3.4
E) 254.342
21. Solve the exponential equation below algebraically. Round your result to three decimal
places.
475
 125
1  ex
A) –0.734 B) 2.275 C) –1.364 D) 0.277 E) 1.030
Learning Objective: Solve exponential equation
Section: 3.4
22. Solve ln x2  ln11  0 for x.
A) 121 B)  11, 11 C) e121 D) e11/ 2 E) no solution
Learning Objective: Solve logarithmic equation
Section: 3.4
23. Determine whether the scatter plot below could best be modeled by a linear model, a
quadratic model, an exponential model, a logarithmic model, or a logistic model.
A) a linear model
D) an exponential model
B) a quadratic model
E) a logarithmic model
C) a logistic model
Learning Objective: Identify type of model for scatter plot
Section: 3.6
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