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CHAPTER 4, FORM E
COLLEGE ALGEBRA
NAME
DATE
1. Consider the function defined by
( )
5f x x=-
. Which of the following 1. ____________
represents the domain and the range of
( )
fx
?
a.
( ) ( )
, ; ,– ¥ ¥ – ¥ ¥
b.
[ ) [ )
0, ; 5,¥¥
c.
( ][ )
,5 ; 0,– ¥ ¥
d.
2. If
, find
( )
1.fx
–
2. ____________
a.
25x–
b.
25x+
c.
25x+
d.
2
5x–
3. Solve
(9 3 )
4 64.
x–=
3. ____________
a.
{ }
2–
b.
{}
1
c.
{ }
2
d.
{ }
3
Write in logarithmic form.
4.
21
39
–=
4. ____________
a.
2
1
log 3 9
–=
b.
2
1
log 3
9
–=
c.
3
1
log 2
9=-
d.
3
1
log 2 9
-=
Write in exponential form.
5.
5
1
log 2
25 =-
5. ____________
a.
1/25
52=-
b.
2
15
25
–
æö
÷
ç=
÷
ç÷
ç
èø
c.
21
525
–=
d.
51
225
-=
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CHAPTER 4, FORM E
Graph each function.
6.
11
2
x
yæö
÷
ç
=+
÷
ç÷
ç
èø
6. ____________
a.
b.
c.
d.
7.
1/ 3
log ( – 2)yx=
7. ____________
a.
b.
c.
d.
112
CHAPTER 4, FORM E
8. Use properties of logarithms to write the following 8. ____________
as a sum, difference, or product of logarithms.
2
8
log wx
y
a.
88
8
1
2log log
2
log
wy
y
+
b.
8 8 8
1
2log log – log
2
w x y+
c.
8 8 8
1
2log log – log
2
w x y
æö
÷
ç÷
ç÷
ç
èø
d.
2
8 8 8
1
2log log – log
2
w x y+
Use a calculator to find approximations for each of the following logarithms. Express answers to three decimal places.
9.
13
log 10
9. ____________
a. 6.195 b. 1.255 c. 0.898 d. 1.477
10.
ln131
10. ____________
a. 0.131 b. 1.892 c. 4.875 d. 6.127
11.
If ( ) and (3) 64, find (–2).
x
f x a f f==
11. ____________
a. –16 b.
1
4
c.
1
16
d.
1
–16
12. What values of x cannot possibly be solutions of the following equation? 12. ____________
log (2 5) –1
ax+=
a.
5
– , – 2
æö
÷
ç¥÷
ç÷
ç
èø
b.
5
– , – 2
æù
çú
¥
ç
çú
èû
c.
5
–,
2
éö
÷
ê¥÷
÷
êø
ë
d.
5
–,
2
æö
÷
ç¥÷
ç÷
ç
èø
13. Between what two consecutive integers must x be
if 2 15?
x=
13. ____________
a. 2 and 3 b. 3 and 4
c. 4 and 5 d. 5 and 6
Use properties of logarithms to solve each equation. Express answers to three decimal places.
14.
log( 9) 1 logxx+ = –
14. ____________
a.
1
2
ìü
ïï
ïï
íý
ïï
ïï
îþ
b.
{ }
1, –1
c
{ }
–1
d.
{}
1
15.
2
5 15
x–=
15. ____________
a.
{ }
–0.317
b.
{ }
3.099
c.
{ }
3.683
d.
{ }
4.807
16.
99
log ( 7) log ( 7) 1xx– + – =
16. ____________
a.
{ }
10,10–
b.
{ }
50
c.
{ }
50–
d.
{ }
10
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CHAPTER 4, FORM E
17. A radioactive substance is decaying so that the number of grams 17. ____________
present after t days is given by the function
–.01
( ) 2000 .
t
A t e=
Find the half-life of the substance to the nearest day.
a. 20 days b. 50 days
c. 5 days d. 69 days
18. The temperature of a liquid t minutes after being placed into 18. ____________
an environment having constant temperature
0
T
is given by
–.14
0
( ) 100 .
t
T t T e=+
How long, to the nearest minute, will it take a cup of hot tea
to cool to a temperature of 20°C in a refrigerator at 5°C?
a. 6 min b. 11 min
c. 14 min d. 5 min
19. How long must $4,500 be in a bank at 2.5% compounded annually 19. ____________
to become $5218.60? (Round to the nearest year.)
a. 6 yr b. 8 yr
c. 9 yr d. 10 yr
20. The population of a town is 2100 and increasing at a rate of 20. ____________
1.3% per year, while the number of cats in the town is currently
1000 and increasing at a rate of 8% per year. Assuming this trend
continues, estimate graphically when the cat population will
exceed the human population in this town.
a. 11.6 yr b. 73.7 yr
c. 52.7 yr d. 14.3 yr
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CHAPTER 4, FORM E