CHAPTER 4, FORM C
COLLEGE ALGEBRA
NAME
DATE
1. Consider the function defined by
( )
4f x x=−
.
a. What are the domain and range of f? 1a._______________________________
b. Find the rule for
( )
1
fx
−
. 1b._______________________________
c. What are the domain and the range of
1
f−
? 1c._______________________________
2. Match the equation with its correct graph:
2
logyx=
2. _______________________________
(a) (b) (c) (d)
Graph the function.
3.
1–1
2
x
y
=
3.
4.
6 2 –1
Solve 8 64 .
xx+=
4._______________________________
5a. Write
2
5 0.04
−=
in logarithmic form. 5a._______________________________
5b. Write
log 5xy=
in exponential form. 5b._______________________________
CHAPTER 4, FORM C
6. Use properties of logarithms to write the following 6._______________________________
as a sum, difference, or product of logarithms.
3
log xz
y
Use a calculator to find approximations for each of the following logarithms. Express answers to three decimal
places.
7.
ln 35.15
7._______________________________
8.
ln 0.28y=−
8._______________________________
9.
1.5
log 78.3
9._______________________________
10.
If ( ) and (6) 64,
x
f x a f==
find the following values of f (x).
a. f (4) 10. a._______________________________
b. f (–3) b._______________________________
11. What values of x cannot possibly be solutions of 11._______________________________
the following equation?
log (3 – 5) 4
ax=
Use properties of logarithms to solve each equation. Express answers to three decimal places.
12.
ln( 4 ) ln3 ln(2 )xx– – + = –
12._______________________________
13.
66
log ( 5) log 2xx+ + =
13._______________________________
14.
9
ln – 3ln 2 lnxx
=
14._______________________________
15.
log log5 log 2 log( 3)xx– = – –
15._______________________________
16. Between what two consecutive integers must x be 16._______________________________
if 3 28?
x=
Explain why this is so. _______________________________
17. The amount of a radioactive substance present after
t seconds is given by the function
–.03
( ) 4000 ,
t
A t e=
a. How many grams of the substance, to the nearest 17. a.___
tenth of a gram, will be present after 21 sec?
b. Find the half-life of the substance to the nearest b._______________________________
tenth of a second.
18. The temperature of a liquid t minutes after being 18._______________________________
placed into an environment having constant temperature
0
T
is given by
–.1
0
( ) 100 .
t
T t T e=+
How long, to the nearest minute, will it take a cup of hot
coffee to cool to a temperature of 20°C in a refrigerator
at 5°C?
CHAPTER 4, FORM C
19. How many years, to the nearest tenth, will be needed for 19._______________________________
$4000 to increase to $9000 at 1.8% compounded monthly?
20. The population of a town is 1750 and increasing at a 20._______________________________
rate of 1.5% per year, while the number of cats in the
town is currently 625 and increasing at a rate of 9% per year.
Assuming this trend continues, estimate graphically when
the cat population will exceed the human population in
this town.
CHAPTER 4, FORM C