Page 1
1.
Find a value for a to make the inequality true:
1
8 17,100 8
aa+
2.
Expand the following expression using rules of logarithms:
( )
65
log A B
3.
Expand the following expression using rules of logarithms:
( )
63
log x y
A)
log(6x) log(3y)+
B)
( )
63
log x y+
C)
6 log(x) 3 log(y)+
D)
log(6x 3y)+
4.
Contract the following expression using rules of logarithms. Express your answer as a
single logarithm.
4 log(A) 6 log(B)+
5.
Contract the following expression using rules of logarithms. Express your answer as a
single logarithm.
log(a) 6 log(b)+
A)
( )
log a 6b+
B)
( )
6
log a b+
C)
( )
log a 6b
D)
( )
6
log a b
6.
Expand the following expression using rules of logarithms:
5
2
A
log B
Page 2
7.
Expand the following expression using rules of logarithms:
2
5
m
log n
A)
log(2m) log(5n)−
B)
( )
25
log m n−
C)
log(2m 5n)−
D)
2 log(m) 5 log(n)−
8.
Contract the following expression using rules of logarithms. Express your answer as a
single logarithm.
3 log(x) 5 log(y)−
9.
Contract the following expression using rules of logarithms. Express your answer as a
single logarithm.
2 log(m) log(n)−
A)
2m
log n
B)
( )
log 2m n−
C)
2
m
log n
D)
( )
2
log m n−
10.
Expand the following expression using rules of logarithms:
4
2
mn
log p
11.
Expand the following expression using rules of logarithms:
64
5
mn
log p
A)
log(6m 4n 5p)+−
B)
6 log(m) 4 log(n) 5 log(p)+−
C)
6 4 5
log(m n p )+−
D)
log(6m) log(4n) log(5p)+−
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12.
Contract the following expression using rules of logarithms. Express your answer as a
single logarithm.
5 log(a) log(b) 5 log(c)+−
13.
Contract the following expression using rules of logarithms. Express your answer as a
single logarithm.
3 log(A) 2 log(B) 3 log(C)+−
A)
32
3
AB
log C
B)
( )
log 3A 2B 3C+−
C)
( )
3 2 3
log A B C+−
D)
3A 2B
log 3C
14.
Expand the following expression using rules of logarithms:
( )
log –2 A+ 2
15.
Expand the following expression using rules of logarithms:
( )
log 4A+6
A)
( )
1log 4A+6
2
B)
( )
1
log 4A+6
2
C)
( )
log 4A+6
D)
( )
log 4A + 6
16.
Contract the following expression using rules of logarithms. Write your answer as a
single logarithm.
( )
1log m–1
2
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17.
Contract the following expression using rules of logarithms. Write your answer as a
single logarithm.
( )
1log 3a–1
2
A)
( )
log 3a–1
B)
( )
log 3a–1
C)
( )
1
log 3a–1
2
D)
3 log a –1
18.
Expand the following expression using rules of logarithms:
( )
( )
log 5a– 2 2 a+ 3
19.
Expand the following expression using rules of logarithms:
( )
( )
log 4A+1 2A+8
A)
( ) ( )
( )
1log 4A+1 log 2A+8
2+
B)
( ) ( )
1
log 4A+1 log 2A+8
2
+
C)
( ) ( )
log 4A+1 log 2A+8+
D)
( ) ( )
1
log 4A+1 log 2A+8
2
+
20.
Contract the following expression using rules of logarithms. Write your answer as a
single logarithm.
( ) ( )
1
log a+ 4 log 2a– 8
2
+
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21.
Contract the following expression using rules of logarithms. Write your answer as a
single logarithm.
( ) ( )
1
log –5a– 4 log 2a+ 6
2
+
A)
( )
( )
log –5a– 4 2a+ 6+
B)
( ) ( )
1
log –5a– 4 2a+ 6
2
+
C)
( )
( )
log –7 a+ 8
D)
( )
( )
log –5a– 4 2a+ 6
22.
Solve the equation for t.
( )
51 1.82 560
t=
Round your answer to 2 decimal places.
23.
Which of the following is the exact solution to the equation?
( )
17 1.58 139
t=
A)
( )
log 139
log(17 1.58)
t=
B)
( )
log 139
log(17) log(1.58)
t=
C)
139
log 17
log(1.58)
t
=
D)
139
17 log(1.58)
t=
24.
The function,
( )
5,000 1.06 t
V=
, gives the value, V, of an investment t years after the
initial investment. How many years until the investment is worth $420,000?
Round your answer to the nearest year.
25.
The function,
( )
3,500 1.01 t
V=
, gives the value, V, of an investment t years after the
initial investment. How many years until the value of the investment doubles?
Round your answer to the nearest year.
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26.
Upon her retirement, Mary begins to receive money from a retirement account. The
function,
( )
830,000 0.93 t
M=
, gives the money remaining, M, in the account t years
after her retirement. How many years until the account balance is $490,000?
Round your answer to the nearest year.
27.
Upon her retirement, Mary begins to receive money from a retirement account. The
function,
( )
510,000 0.83 t
M=
, gives the money remaining, M, in the account t years
after her retirement. How many years until Mary has received half of the money from
the account?
Round your answer to the nearest year.
28.
The number of people, N, visiting a particular web site increases 10% each week. If the
web site had 90,000 visitors this week, how many weeks until the number of people
reaches 340,000?
Round your answer to the nearest week.
29.
The number of people, N, visiting a particular web site increases 8% each week. If the
web site had 20,000 visitors this week, how many weeks until the number of people
doubles?
Round your answer to the nearest week.
30.
Radium-226 has a half-life of 1600 years. If a fossil has 44% of it’s original Radium-
226 left, how old is it?
Round your answer to the nearest tenth of a year.
31.
Solve the equation for x.
log( ) 3x=
32.
Solve the equation for x.
log( ) 0.3x=
Round your answer to 2 decimal places.
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33.
Which of the following is the exact solution of the equation?
log( ) 0.4x=
A)
0.4
xe=
B)
0.4
log(10)
x=
C)
log(0.4)x=
D)
0.4
10x=
34.
Solve the equation for x.
log( – 6) 0.3x=
Round your answer to 2 decimal places.
35.
Which of the following is the exact solution of the equation?
log( +1) 2.5x=
A)
2.5–1
10x=
B)
2.5
10 –1x=
C)
log(2.5) –1x=
D)
2.5
log(1)
x=
36.
Solve the equation for x.
log( – 2) log(4) 2.3x+=
Round your answer to 2 decimal places.
37.
Which of the following is the exact solution of the equation?
log( – 2) log(5) –0.5x+=
A)
–0.5
10 + 2
5
x=
B)
–0.5
10 – 3.5x=
C)
–0.5
10 +3x=
D)
–0.5
10 +10
5
x=
Page 8
Answer Key
Page 9