Dugopolski’s 49College Algebra
Chapter 4 Test — Form A Name:_________________________
Simplify each expression.
1. 2. 3. log log
ln( )
1. _______ 2. _______ 3. _______
Write each expression as a single logarithm.
4. 5. log ( ) log log log(49) 3 log( )
4. _____________________ 5. _____________________
Find the exact solution to each equation.
6 7.. 2 log log log
6. _____________________ 7. _____________________
8. log log
8. _____________________
Find an approximate solution (to 4 decimal places) for each equation.
9. 10 3 = 4 . log 41 = 2
9. _____________________ 10. _____________________
50 Form 4A
Graph each equation in the -plane.
11 12.. log
Solve each problem.
13. Find , if and .
13. _____________________
14. A student has found a great investment deal. She has found a way to receive an annual
interest rate of 12% compounded quarterly. If she has $600 to invest now and wants to end
up with $1000 from this investment, how long would it be before she reaches that value?
Round to the nearest tenth of a year.
14. _____________________
15. The radioactive element decays exponentially. After 7 hours, 35 grams have decayed
to 20 grams. What is the rate of decay (to the nearest hundredth) for ?
15. _____________________
16. Find ( ) if
16. _____________________
Dugopolski’s 51College Algebra
Chapter 4 Test — Form B Name: _________________________
Simplify each expression.
1. 2. 3. log log ln
1. _______ 2. _______ 3. _______
Write each expression as a single logarithm.
4. 5. log log log log (8) 2 log
4. _____________________ 5. _____________________
Find the exact solution to each equation.
6. 7. 25 = 125 3 log log
6. _____________________ 7. _____________________
8. log log
8. _____________________
Find an approximate solution (to 4 decimal places) for each equation.
9. 10. 4 = 3 log (20) = 2
9. _____________________ 10. _____________________
52 Form 4B
Graph each equation in the -plane.
11 12.. log
Solve each problem.
13. Find , if and .
13. _____________________
14. A student has found a great investment deal. She has found a way to receive an annual
interest rate of 8% compounded semiannually. If she has $600 to invest now and wants to
end up with $1000 from this investment, how long would it be before she reaches that
value? Round to the nearest tenth of a year.
14. _____________________
15. The radioactive element decays exponentially. After 5 hours, 35 grams have decayed
to 20 grams. What is the rate of decay (to the nearest hundredth) for ?
15. _____________________
16. Find if 3 .
16. _____________________
Dugopolski’s 53College Algebra
Chapter 4 Test — Form C Name: _________________________
1 2.. Change 3 to logarithmic form. Change ln to exponential form.
1. _____________________ 2. _____________________
Simplify each expression.
3. 4. 5. log (25) log
ln
3. _________ 4. _________ 5. _________
Find the exact solution to each equation.
6 7.. 8 = 16 log log log
6. __________________ 7. __________________
8. log log
8. __________________
Find an approximate solution (to 4 decimal places) for each equation.
9. 10. log ( )
9. __________________ 10. __________________
54 Form 4C
Graph each equation in the -plane.
11. 12 . ln
Let , , and . Evaluate each of the following.
13 14. 15..
13. _______ 14. _______ 15. _______
Solve each problem.
16. Rewrite the following as a sum and/or difference of multiples of logarithms:
ln .
16. __________________________________
17. Find the -intercept for the graph of Give the exact value.
17. _________________
18. A radioactive substance decays exponentially at a rate 0.000512. How many grams
are left after 50 years from a 10-gram specimen?
18. _________________
Dugopolski’s 55College Algebra
Chapter 4 Test — Form D Name: _________________________
1. 2.Change 5 to logarithmic form. Change log to exponential form.
1. _____________________ 2. _____________________
Simplify each expression.
3. 4. 5. log (2) log
ln(2)
3. _________ 4. _________ 5. _________
Find the exact solution to each equation.
6. 7 = 100 . log log log
1
10
6. __________________ 7. __________________
8. log log
8. __________________
Find an approximate solution (to 4 decimal places) for each equation.
9. 10. log ( )
+
9. __________________ 10. __________________
56 Form 4D
Graph each equation in the -plane.
11 12.. ln
Let , , and ( ) = . Evaluate each of the following.
13. 14. 15 .
13. _______ 14. _______ 15. _______
Solve each problem.
16. Rewrite the following as a sum and/or difference of multiples of logarithms:
ln .
16. ___________________________________
17. Find the -intercept for the graph of Give the exact value.
17. _________________
18. A radioactive substance decays exponentially at a rate 0.000512. How many grams
are left after 200 years from a 10-gram specimen?
18. _________________
Dugopolski’s 57College Algebra
Chapter 4 Test — Form E Name: _________________________
Multiple Choice: Choose the best answer for each of the following.
____ 1. If , then when equals what value?
a. b. 2 c. d.
____ 2. The range of the function is given by:
a. ( , 1) b. (1, ) c. ( , 1) d.( , )
____ 3. A student wishes to invest $100 in a savings account yielding 2% annual
interest compounded every 6 months. How much will his investment be worth
at the end of 1 year?
a. $101.01 b. $102.01 c. $104.00 d. $102.02
____ 4. The number of grams of a radioactive substance, , remaining years after
January 1, 2015, is given by the formula: Find the number of
grams present on January , 2020.
a. Less than 1 gram b. 53 grams c. 57 grams d. 6 grams
____ 5. Evaluate log
a. b. c. d.
____ 6. Find the domain of log
a. ( 1, ) b. ( 1, ) c. (0, ) d. ( )
____ 7. Solve for :
a. log b. log (4) c. 2 d. log
2
____ 8. Solve for : log log
a. 5 b. 3 or c. 3 d. 1
____ 9. Rewrite as a sum or difference of multiples of logarithms and simplify:
log
a. log log c. 0.5 log ( )
log ( )
b. log log log d. 0.45
58 Form 4E
____ 10. Solve for , rounding to four decimal places: =
a. 82.4361 b. 0.5101 c. 34.6574 d. 25
____ 11. Solve for rounding to four decimal places: log ,
a. 2.8218 b. 10941.0480 c. 2.8105 d. 0.1351
____ 12. Which of the following statements are true?
A. ln ln D. log
B. log log
C. log E. log log (4)
log
log
a. D and E only b. B and C only c. A and E only d. B and D only
____ 13. Solve for log log:
a. b. c. d.
____ 14. Radioactive element decays exponentially at a rate of 4% per year. If we
begin with 5 grams of , how long (to the nearest tenth of a year) will it take
for only 3 grams to remain?
a. 45.6 years b. 13.0 years c. 0.7 year d. 12.8 years
____ 15. Solve for :
a. b. c. d.
____ 16. The population of insects on one square mile in Alaska appears to be growing
due to a warming trend in the region according to the formula:
ln , where is the time in years from the present.
In how many years will there be 18000 insects in this region? Round to the
nearest tenth of a year.
a. 3.2 years b. 6.7 years c. 35056 years d. 2299 years
Dugopolski’s 59College Algebra
Chapter 4 Test — Form F Name:_________________________
Multiple Choice: Choose the best answer for each of the following.
____ 1. If , then when equals what value?
a. b. c. d.
____ 2. The range of the function is given by:
a. ( , 3) b. (2, ) c. ( , 2) d. ( , 2)
____ 3. A student wishes to invest $500 in a savings account yielding 3% annual
interest compounded every 6 months. How much will his investment be worth
at the end of 1 year?
a. $506.02 b. $515.00 c. $515.11 d. $515.19
____ 4. The number of grams of a radioactive substance, , remaining years after
January 1, 2015, is given by the formula: Find the number of
grams present on January , 2020.
a. Less than 1 gram b. grams c. grams d. grams
____ 5. Evaluate log ( ).
a. 4 b. c. d. 27
____ 6. Find the domain of log
a. 0, b. , c. , d.
____ 7. Solve for :
a. log b. log (4) c. 2 d. log
2
____ 8. Solve for : log log
a. or b. c. d.
____ 9. Rewrite as a sum or difference of multiples of logarithms and simplify:
log
a. c. log ( )
log ( )
b. log log log d. log log
60 Form 4F
____ 10. Solve for , rounding to four decimal places: =
a. b. c. d.
____ 11. Solve for rounding to four decimal places: log ,
a. b. c. d.
____ 12. Which of the following statements are true?
A. ln ln D. log
B. log log
C. log E. log log (4)
log
log
a. D and E only b. B and C only c. A and E only d. B and D only
____ 13. Solve for log log :
a. b. c. d.
____ 14. Radioactive element decays exponentially at a rate of 3% per year. If we
begin with 5 grams of , how long (to the nearest tenth of a year) will it take
for only 3 grams to remain?
a. 200 years b. 59.7 years c. 17.0 years d. 1.7 years
____ 15. Solve for :
a. b. c. d.
____ 16. The population of insects on one square mile in Alaska appears to be
growing due to a warming trend in the region according to the formula:
ln , where is the time in years from the present.
In how many years will there be 18000 insects in this region? Round to the
nearest tenth of a year.
a. 6.7 years b. 35056 years c. 2299 years d. 3.2 years
Dugopolski’s 119College Algebra
Chapter Test Keys
CHAPTER 4
120 Chapter 4 Test Key