Name:
Period:
D
College Algebra: Expos and Logs Test (4.5 - 4.8)
You must show supporting work on all problems to receive credit. Calculators are required.
I  Pr t
r

A  P0 1  
n

nt
A  A0 e kt
A  P0 e rt
 t   T   0  T e kt
In problems 1 - 5, choose the one alternative that best completes the statement or answers the question.
Supporting work/reasoning must be shown in order to receive credit for your answer. (+2 ea)
2
 50 
1. If log 6 2  a, log 6 3  b , and log 6 5  c , log 6   can be written in terms of a, b, and c as
 9 
A.
B.
C.
D.
E.
1. ________
4c + 2a - 2b
4c + 2a - 4b
2c + 2a - 4b
4c + a - 2b
None of the above
2. The half-life of radioactive cobalt is 6.2 years. If a sample presently contains 100 grams of radioactive
cobalt now, how much will be present in 12 years?
2. ________
A.
B.
C.
D.
E.
10.5 grams
26.1 grams
14.1 grams
approximately zero grams
None of the above
3. The formula D  11e 0.4h can be used to find the number of milligrams D of a certain drug that is in a
patient's bloodstream h hours after the drug has been administered. The drug is to be administered again when
the amount in the bloodstream reaches 4 milligrams. What is the time between injections?
A.
B.
C.
D.
E.
about 0.8 of an hour
about 3.1 hours
about 2.2 hours
about 2.5 hours
None of the above
2
4. The exact value of log 3 3  log 16 42  log 16 21  log 6 6
3. ________
4. ________
A. 13
4
B. 7
C. 11
4
D. -1
E. None of the above.
5. What does the point (2, 1/2) of the parent function become when transformed by f ( x)  1  log 4  2x  2?
A. (-5, 1/2)
B. (-2, 1/2)
5. ________
C. (2, -1/2)
D. (-5, 3/2)
E. None of the above
Solve the following logarithmic equations algebraically. No decimal answers will be accepted.
6. 2 log 3 ( x  3)  log 3 8  2
7. ln 15  ln( 8  x)  ln x
6. __________ (+5)
7. __________ (+5)
8. log 18 ( x  3)  log 7 7   log 18 (2 x  1)
9. 3 log 4 ( x)  log 16 x  14
8. __________ (+5)
9. __________ (+5)
Solve the following exponential equations algebraically. If applicable, give logarithmic answers in terms of
natural log, ln. Combine log expressions to a single logarithm when applicable.
10. 5
3x
4
4 x 1
e x  12e  x
11.
1
7
10. _________________ (+5)
11. _________________ (+5)
x
x2
12. 16  4  48  0
x
x
13. 4  8 
2 x  31
64
12. _________________ (+5)
13. _________________ (+5)
14. Write as a sum and/or difference of logarithms. Express all powers as factors, factor completely, and
combine like terms.

 (2 x  6) 5 x 2  4
ln 
2
 x 2  x  6




14. ______________________________________________________________________ (+5)
In 15 - 17, to receive credit for your answer, you must clearly state all formulas used and show all
relevant algebraic work required to support your answer.
15. Assume the average selling price of a home in Fort Collins grows according to uninhibited exponential
growth. If the average selling price of a home was $35,600 at the start of 1976 and it was $206,400 at the start
of 2007, what can you predict the average selling price of a home in Fort Collins will be in the year 2030?
Round to the nearest dollar.
15. _____________________ (+3)
16. Assume your parents invest $10,000 into a stock fund when you are born to be used for your college
education. The investment does well, on average, and the value grows at 4% compounded monthly.
a) How much will the investment be worth on your 18th birthday? Round to the nearest dollar.
a) ______________ (+2)
b) How many years will it take for the bond to double in value? Round to one decimal place.
b) _____________ (+2)
c) How much would you have had to invest initially in order for the investment to be worth $40,000 on your
18th birthday? Round to the nearest dollar.
c) ______________ (+2)
d) If instead, the investment is compounded continuously at 4%, how many years will it take for the investment
to triple in value? Round to one decimal place.
d) _____________ (+2)
17. “Bananas Foster” is a dessert served flambe' style at your table featuring banana slices cooked in a vanilla,
brown sugar, and cinnamon cream sauce. Assume the heated banana slices are initially 325 °F and the room
temperature is 62 °F. After 5 minutes, the temperature of the bananas is 225 °F. If you cannot eat the banana
slices until they cool to 175 °F, how many minutes will you have to wait before you can eat your dessert?
Round answer to the nearest minute.
17. _____________________ (+3)