Exponents - Gwendolyn Brooks College Prepatory Academy · 2015-02-22 · Name : Score : Printable...
Transcript of Exponents - Gwendolyn Brooks College Prepatory Academy · 2015-02-22 · Name : Score : Printable...
Name: __________________________ Score:
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Find the value of x to balance the equation.
1) �� = 343
� = __________________
2) 1024 = 2�
� = __________________
3) 512 = ��
� = __________________
4) 729 = 3�
� = __________________
5) 225 = ��
� = __________________
6) �� = 1331
� = __________________
7) �� = 196
� = __________________
8) 625 = ��
� = __________________
9) 1024 = 4�
� = __________________
10) 32 = 2�
� = __________________
11) �� = 729
� = __________________
12) 1728 = ��
� = __________________
13) �� = 1296
� = __________________
14) 1000 = ��
� = __________________
15) 256 = 2�
� = __________________
16) 243 = 3�
� = __________________
17) �� = 169
� = __________________
18) 216 = ��
� = __________________
19) 64 = ��
� = __________________
20) 125 = 5�
� = __________________
21) �� = 49
� = __________________
Exponents
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Find the value of x to balance the equation.
1) 36 = ��
� = __________________
2) 81 = 3
� = __________________
3) �� = 512
� = __________________
4) 256 = 4
� = __________________
5) 2744 = ��
� = __________________
6) �� = 81
� = __________________
7) 2197 = ��
� = __________________
8) �� = 100
� = __________________
9) 2187 = 3
� = __________________
10) �� = 2401
� = __________________
11) 144 = 12
� = __________________
12) 25 = ��
� = __________________
13) 729 = 9
� = __________________
14) 512 = ��
� = __________________
15) �� = 243
� = __________________
16) 169 = ��
� = __________________
17) �� = 128
� = __________________
18) 243 = 3
� = __________________
19) �� = 121
� = __________________
20) 3375 = 15
� = __________________
21) 64 = ��
� = __________________
Exponents
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Find the value of x to balance the equation.
1) −1728 = ��
� = __________________
2) �� = 729
� = __________________
3) 256 = (−4)�
� = __________________
4) �� = −128
� = __________________
5) 225 = (−15)�
� = __________________
6) 169 = ��
� = __________________
7) 125 = 5�
� = __________________
8) 1024 = ���
� = __________________
9) �� = 256
� = __________________
10) 36 = ��
� = __________________
11) �� = −216
� = __________________
12) 64 = (−8)�
� = __________________
13) �� = 1331
� = __________________
14) 81 = (−3)�
� = __________________
15) 100 = ��
� = __________________
16) 64 = (−2)�
� = __________________
17) 2401 = ��
� = __________________
18) �� = −343
� = __________________
19) −8 = ��
� = __________________
20) �� = 3375
� = __________________
21) 1296 = (−6)�
� = __________________
Exponents
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Find the value of x to balance the equation.
1) �� = 2187
� = __________________
2) 16 = (−4)�
� = __________________
3) 256 = ��
� = __________________
4) 625 = (−5)�
� = __________________
5) −512 = ��
� = __________________
6) �� = 36
� = __________________
7) −1024 = ��
� = __________________
8) �� = 729
� = __________________
9) 2401 = (−7)�
� = __________________
10) �� = 64
� = __________________
11) 27 = 3�
� = __________________
12) 2197 = ��
� = __________________
13) 121 = (−11)�
� = __________________
14) 225 = ��
� = __________________
15) �� = 1296
� = __________________
16) −1331 = ��
� = __________________
17) �� = 1000
� = __________________
18) 144 = 12�
� = __________________
19) �� = −125
� = __________________
20) 196 = (−14)�
� = __________________
21) −2197 = ��
� = __________________
Exponents
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Find the value of x to balance the equation.
1)�� = − 1512
� = __________________
2)34327 = �73��
� = __________________
3)� 111���
= 121
� = __________________
4)256 = 2�
� = __________________
5)729 = ��
� = __________________
6) − 64125 = ��
� = __________________
7)�� = −512125
� = __________________
8) − 8343 = �−2
7��
� = __________________
9)� 114���
= 196
� = __________________
10)169 = (−13)�
� = __________________
11) 1343 = ��
� = __________________
12) − 216 = ��
� = __________________
13)�� = −2764
� = __________________
14)64 = (−2)�
� = __________________
15)�15���
= 625
� = __________________
16)81 = (−9)�
� = __________________
17)512 = ��
� = __________________
18)72964 = ��
� = __________________
19)�� = 125216
� = __________________
20) 27512 = �38��
� = __________________
21)�59���
= 8125
� = __________________
Exponents
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Find the value of x to balance the equation.
1)�� = 1024
� = __________________
2)6561256 = −94�
�
� = __________________
3) − 17�
��= − 1
343
� = __________________
4)2197 = 13�
� = __________________
5) − 125 = ��
� = __________________
6) 2433125 = ��
� = __________________
7)�� = −3375
� = __________________
8)12962401 = 67��
� = __________________
9)10�� = 1000
� = __________________
10)729 = 9�
� = __________________
11) 149 = ��
� = __________________
12) − 1331 = ��
� = __________________
13)�� = −125216
� = __________________
14)1296 = �−6)�
� = __________________
15) 27���
= 240116
� = __________________
16) − 32 = �−2)�
� = __________________
17) 116 = ��
� = __________________
18) − 2764 = ��
� = __________________
19)�� = 512729
� = __________________
20) − 8343 = −2
9��
� = __________________
21) 45���
= 256625
� = __________________
Exponents
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Solve for x.
Example 1: Example 2:
log4 x = 2
4� = x
log5 25 = x
5� = 25
5� = 5
�x = 2
x = 16
Solve for x.
1) log� 32 = 5
x =
2) log3 x = 3
x =
3) log3 = x
x =
4) log5 = x
x =
181
125
7) log9 x =
x =
8) log� 2 =
x =
1 2
1 3
9) log6 x = 2
x =
10) log4 256 = x
x =
5) log� 36 = 2
x =
6) log2 x = 4
x =
Logarithm - Solve
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Solve for x.
Example 1: Example 2:
log4 = x
Solve for x.
2) log6 x = 3
x =x =
1) log� 4 = 2
4) log8 = x
x =
164
3) log10 = x
x =
11000
8) log25 x =
x =
1 2
7) log5 x = 2
x =
10) log2 x = 8
x =
9) log� 49 = 2
x =
6) log� 81 = 4
x =
5) log5 625 = x
x =
1 16
4� = 1
164
� �4
� =
x = –2
log� 81 = 4
x�
= 3�
x = 3
x�
= 81
Logarithm - Solve
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Solve for x.
Example 1: Example 2:
log2 = xlog2 x = 3
2� = x
x = 8
Solve for x.
x =
3) log9 = x181
4) log5 x = 3
x =
132
2) log4 x = 2
x =
1) log3 27 = x
x =
8) log� 3 =
x =
1 3
7) log16 x =
x =
1 2
10) log� 64 = 2
x =
9) log7 x = 2
x =
6) log2 = x
x =
5) log� 100 = 2
x =
1 82
� = 1
82
�̄2
� =
x = –3
Logarithm - Solve
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Solve for x.
Example 1: Example 2:
log5 x = 2log64 4 = x
64� = 4
4� �
= 4
Solve for x.
5� =
x = 625x = 1 3
12 � 12
5�
= x
1) log4 2 = x 2)
x = x =
log� 64 = 213
3) log6 = x 4) log2 = x16
116
x = x =
5) log = x 6) log� 3 =
x = x =
12
1 8
7) log� 6 = 1 2
x = x =
8) log3 x = 213
9) log4 x = 3 10) log125 25 = x
x = x =
14
Logarithm - Solve
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Solve for x.
Example 1: Example 2:
log� 2ˉ2 = –1log81 9 = x
81� = 9
9� �
= 9
Solve for x.
x =
x = 1 2
xˉ1 = � � �4
5) log = x 6) log32 8 = x
x = x =
18
1 4
7) log� 6 = 1 3
x = x =
8) log� 16 = 114
3) log128 = x 4) log4 = x14
12
x = x =
9) log5 x = 3 10) log27 3ˉ2 = x
x = x =
1) 2)
x = x =
log2 x = 215 log� 5 = 1
3
Logarithm - Solve
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Solve for x.
Example 1: Example 2:
log25 5�̄ = xlog3
Solve for x.
x =
25� =
� � �5
� �=
� � �
1 3
= �31� �
= � � �� �
=
x = –13 2
–
1) log49 7 = x 2)
x = x =
log� 81 = 212
3) log81 = x 4) log8 = x13
12
x = x =
5) log = x 6) log25 625 = x
x = x =
132
1 2
9) log8 x = 3 10) log� 2ˉ4 = –1
x = x =
7) log� 5 = 1 2
x = x =
8) log7 x = 223
Logarithm - Solve
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Evaluate each expression.
Example :Evaluate the expression :
log� b� = c log� b
log� a = 1
Answer Answer
Answer Answer
Answer Answer
Answer Answer
Answer Answer
.
4) log81 92 log49 7
7) log16 4 – log8 2ˉ31 6
9) log36 6ˉ4 log81 35.
log 2 log64 4 181
13
.log 2 log64 4 = log log64 64181
13
14 181
181
23
.
1 6
=
1) log 6 log81 3 .136
2) log 5 + 4 log32 2125
3) log 3 – log16 12127
5) log125 5 3 log 6.136
6) log32 + 3 log612
136
8) 3 log49 72 log 4116
10) log + 5 log32 21 4164
Evaluating Expressions
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Evaluate each expression.
Example :
log� b� = c log� b
Evaluate the expression : log16 44 + log 3ˉ1
log� a = 1
Answer Answer
Answer Answer
Answer Answer
Answer Answer
Answer Answer
=
1) log 4 – log25 5ˉ21 2
127log16 44 + log 3ˉ1 = log16 162 + log127 127
127
13
13
= 2(1) + (1)
73
1322) log log81 91
4.
164
3) 5 log27 3log 5125
4) log + 6 log8 21 6136
5) log 64 + 7 log125 5 12
6) log 3 – 4 log64 819
7) 3 log 16 log36 6. 14
8) log32 2log 616
9) log81 36 + 2 log 14411210) log128 2 – log 73
149
Evaluating Expressions
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Evaluate each expression.
Example :
log� b� = c log� b
log� a = 1
Answer Answer
Answer Answer
Answer Answer
Answer Answer
Answer Answer
1) 2 log27 39 log64 4
.
4) log – 8 log121 1119
181
.5) log 9 log49 716414
6)4 log5 1256 log64 8
7) log – 5 log4 1616
1 36
9) log + 3 log144 121 4917
Evaluate the expression : log128 2ˉ3 – 4 log 125
15
log128 2ˉ3 – 4 log = – log128 128 – log125
15
37
42 125
125
177
–=
3) log 63 + log2 128136
8) log + 9 log4 213
19
10) log – 4 log9 3181
13
2) log 2 5 log3 243132
Evaluating Expressions
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Solve for x.
Example 1: Example 2:
log4 = 2xlog� � � 27 = 3
(x–1)�
= 27
(x–1)�
= 3�
Solve for x.
2) log3 (x+3) = 4
x =x =
1) log� � 25 = 1
4) log4 = x–5
x =
116
3) log7 49 = 2x+6
x =
8) log4 (x–9) = 4
x =
7) log5 = 3
x =
10) log2 (3x+2) = 5
x =
9) log2� 144 = 2
x =
6) log� � � � (729) = 3
x =
5) log2 8 = 3x
x =
1 16
4� �
= 1 16
4
4� �
=x = –1
x–1 = 3
x = 4
x2
Logarithm - Solve
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Solve for x.
Example 1: Example 2:
log3 (x–4) = 3
3� = x–4
log5 25 = x+2
5� � �
= 25
5� � �
= 5�
x = 0 x = 31
Solve for x.
1) log� � � (16) = 4
x =
2) log5 5x = 3
x =
3) log6 = x–2
x =
4) log2 = 2x+4
x =
136
164
7) log9 (x–1) =
x =
8) log3� 81 = 4
x =
1 2
9) log7 (x+7) = 2
x =
10) log2 32 = x+9
x =
5) log8� 256 = 2
x =
6) log3 = 3
x =
27 = x–4
x4
Logarithm - Solve
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Solve for x.
Example 1: Example 2:
log8 (2x)� = 2log3
Solve for x.
8� = (2x)
�1 3
= x–5
31� � � � � �
= � � � � � � � �
=
x = 4
1) log36 6 = x+3 2)
x = x =
log3 64 = 2
3) log32 = x–1 4) log3 = 2x14
19
x = x =
5) log = 6) log25 625 = 2x+3
x = x =
132
x 8
9) log9 (x–1) = 3 10) log2 2ˉ4 = 2
x = x =
7) log � � 16 = 4
x = x =
8) log6 (4x) = 212
13(8�) = 2x4 = 2xx = 2
15
Logarithm - Solve
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Solve for x.
Example 1: Example 2:
log4 4x = 2log64 4 = x+2
(64)� � �
= 44
� � � � = 4
Solve for x.
4� =
x = 64
12 � � � 12
4
= 4x
1) log4 2 = x–5 2)
x = x =
log� � (27) = 3
3) log2 = 2x+1 4) log4 = 14
116
x = x =
5) log = 4x 6) log5� 8 = 3
x = x =
13
19
7) log� � � (16) = 1 2
x = x =
8) log3 (x+4) = 113
9) 2 log4 (x–2) = 4 10) log128 2 = x+3
x = x =
x = 5 3
–
3x+6 = 1
x2
Logarithm - Solve
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Solve for x.
Example 1: Example 2:
log2 = 3xlog2 (x+6) = 5
2� = x+6
x = 26
Solve for x.
x =
3) log2 = 5x132
4) log2 = 6
x =
116
2) log10 (x+4) = 2
x =
1) log3 81 = 2x–4
x =
8) log4� 2 =
x =
1 3
7) log3 3x = 4
x =
10) log� � � (243) = 5
x =
9) log6 (x–3) = 2
x =
6) log4 = x+4
x =
5) log� � � (125) = 3
x =
1 82
� � = 1
82
�̄2
� � =
x = –1
32 = x+6
x2
Logarithm - Solve
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Solve for x.
Example 1: Example 2:
log2� 2ˉ4 = –2log49 7 = x+3
(49)� � �
= 7(7
� � � � � = 7
Solve for x.
x = x = –5 2
2xˉ2 = 2ˉ4
2
5) log = x+1 6) log16 8 = 2x+2
x = x =
18
1 2
7) log3� 3 = 14
x = x =
8) log� � � (16) = 212
3) log128 = 4) log2 = 5xx4
18
x = x =
9) log6 (3x–3) = 3 10) log27 3ˉ3 = x–5
x = x =
1) 2)
x = x =
log2 (x–4) =15 log� � � (36) = 2
2xˉ2 = (22)ˉ2
17
15
Logarithm - Solve
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Solve each logarithmic equation.
3) log4 (3x–2) = log4 (x+18)
x =
4) log3 (5x+6) = 2 log3 6
x =
1) log5 (x+7) = log5 (2x+3)
x =
2) log2 (x+20) = log2 2
x =
7) log7 (x+1) = log7 (2x+20)
x =
8) log4 (5x–3) = log4 (2x+36)
x =
5) log6 (2x–1) = log6 27
x =
6) log5 24 = log5 (x+2)
x =
11) log5 (2x+2) = log5 (3x+18)
x =
12) log2 (x+17) = 3 log2 2
x =
9) 3 log3 4 = log3 (x+10)
x =
10) log6 4x = log6 100
x =
Logarithmic Equation
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Solve each logarithmic equation.
3) log2 (x+7) = 3 log2 3
x =
4) log5 (3x+7) = log5 (4x+15)
x =
1) log6 2x = log6 68
x =
2) 2 log3 5 = log3 (x+46)
x =
7) log7 (2x+17) = log7 (x+3)
x =
8) log6 (3x–2) = log6 25
x =
5) log4 (7x–3) = log4 (5x+55)
x =
6) log5 48 = log5 (x+4)
x =
11) log3 (1– 4x) = 2 log3 7
x =
12) log4 (3x–15) = log4 (x+67)
x =
9) log2 (x+5) = 4 log2 2
x =
10) log5 (x+6) = log5 (2x+24)
x =
Logarithmic Equation
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Solve each logarithmic equation.
3) log6 5x = log6 75
x =
4) log5 (7x+3) = log5 (8x+32)
x =
1) log2 (x+4) = 2 log2 8
x =
2) log4 (4x–2) = log4 (2x+34)
x =
7) log3 (3–2x) = 2 log3 9
x =
8) log4 (6x–8) = log4 (4x+56)
x =
5) 2 log3 4 = log3 (x+20)
x =
6) log2 (x–2) = 4 log2 3
x =
11) log7 (x+13) = log7 (2x+3)
x =
12) log6 (3x+12) = log6 3
x =
9) log5 74 = log5 (x+6)
x =
10) log5 (2x+15) = log5 (3x+37)
x =
Logarithmic Equation
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Solve each logarithmic equation.
3) log5 (x+5) – log5 2 = log5 50
x =
4) log3 (73+x) = log3 16 + 2 log3 2
x =
1) log2 (x+3) + log2 (x–3) = log2 91
x =
2) log6 x3+ log6 3 = 4 log6 3
x =
7) log2 6 + log2 (1–x) = 2 log3 6
x =
8) log3 7 = log3 (x+41) – log3 2
x =
5) 2 log8 x + log8 2 = log8 72
x =
6) log2 (x–4) – log2 4 = 5 log2 2
x =
9) log4 (x+4) + log4 5 = log4 (3x–2)
x =
10) log6 x – log6 3 = 2 log6 5
x =
Logarithmic Equation
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Solve each logarithmic equation.
3) log3 (x–8) = log3 14 + 2 log3 3
x =
4) log5 (2x+4) – log5 4 = log5 28
x =
1) log6 x – log6 4 = 3 log6 4
x =
2) log4 (x+6) + log4 3 = log4 (2x–2)
x =
7) log2 (3–x) + log2 5 = 2 log3 5
x =
8) 3 log8 x + log8 4 = log8 256
x =
5) log3 5 = log3 (x+57) – log3 6
x =
6) log2 (x–1) – log2 9 = 4 log2 2
x =
9) log6 x2+ log6 5 = 3 log6 5
x =
10) log2 (x+16) + log2 3 = log2 6
x =
Logarithmic Equation
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Solve each logarithmic equation.
3) log2 (5+x) + log2 2 = 3 log3 2
x =
4) log7 (x–5) – log7 4 = 2 log7 5
x =
1) log3 (x–12) = log3 5 + 2 log3 3
x =
2) log2 (x+4) + 3 log2 2 = log2 (6x+4)
x =
7) log6 x – 2 log6 2 = 4 log6 2
x =
8) log2 (x+12) + log2 4 = log2 12
x =
5) log3 12 = log3 (x+16) – log3 5
x =
6) log2 (2–x) + log2 3 = 2 log3 6
x =
9) log4 (x+4) + log4 2 = log4 (3x–7)
x =
10) 3 log8 x – log8 7 = log8 49
x =
Logarithmic Equation
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� � � � � � � � � �
log7 x+8x+6
= 2
1) 2 log3 x = log3 (12x–36)
x =
2) log2 (x–11) + log2 (x–2) = log2 10
x =
3)
x =
4) log4 (x–5) + log4 (x+5) = log4 24
x =
5) 2 log3 (x–1) = log3 3
x =
6) 2 log8 x = log8 (7x–12)
x =
7) log3 (x+2) + log3 (x–3) = log3 14
x =
8) 2 =
x =
log4 x+7x+5
Logarithmic Equation
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� � � � � � � � � �
log7 x+4x+2
= 2
1) log5 (x–7) + log5 (x–5) = –log5 5
x =
2) log2 (x+1) + log2 (x–1) = log2 24
x =
3) 2 log8 x = log8 (13x –12)
x =
4) log4 (x–3) + log4 (x+1) = log4 5
x =
5) 2 log3 (x–6) = log3 4
x =
6)
x =
7) log6 (x+3) + log6 (x–4) = log6 8
x =
8) 2 log3 x = log3 (3x–2)
x =
Logarithmic Equation
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� � � � � � � � � �1) log4 (x+3) + log4 (x+3) = log4 49
x =
2)
x =
3) 2 log3 (x–4) = log3 4
x =
4) log3 (13x–42) = 2 log3 x
x =
5) log2 (x–5) + log2 (x–8) = log2 28
x =
6) 2 log8 x = log8 (8–2x)
x =
7) 2 =
x =
8) log5 (x+1) + log5 (x–1) = log5 3
x =
log4 x+10x+8
log7 x–36
= log7 3x–10
Logarithmic Equation
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Answers
1) �� = 343
� = �
2) 1024 = 2�
� = ��
3) 512 = ��
� = �
4) 729 = 3�
� = �
5) 225 = ��
� = ��
6) �� = 1331
� = ��
7) �� = 196
� = ��
8) 625 = ��
� = �
9) 1024 = 4�
� = �
10) 32 = 2�
� = �
11) �� = 729
� = �
12) 1728 = ��
� = ��
13) �� = 1296
� = �
14) 1000 = ��
� = ��
15) 256 = 2�
� = �
16) 243 = 3�
� = �
17) �� = 169
� = ��
18) 216 = ��
� = �
19) 64 = ��
� = �
20) 125 = 5�
� = �
21) �� = 49
� = �
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Answers
1) 36 = ��
� = �
2) 81 = 3
� = �
3) �� = 512
� = �
4) 256 = 4
� = �
5) 2744 = ��
� = ��
6) �� = 81
� = �
7) 2197 = ��
� = ��
8) �� = 100
� = ��
9) 2187 = 3
� = �
10) �� = 2401
� = �
11) 144 = 12
� = �
12) 25 = ��
� = �
13) 729 = 9
� = �
14) 512 = ��
� = �
15) �� = 243
� = �
16) 169 = ��
� = ��
17) �� = 128
� = �
18) 243 = 3
� = �
19) �� = 121
� = ��
20) 3375 = 15
� = �
21) 64 = ��
� = �
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Answers
1) −1728 = ��
� = −��
2) �� = 729
� = �
3) 256 = (−4)�
� = �
4) �� = −128
� = −�
5) 225 = (−15)�
� = �
6) 169 = ��
� = ��
7) 125 = 5�
� = �
8) 1024 = ���
� = �
9) �� = 256
� = �
10) 36 = ��
� = �
11) �� = −216
� = −�
12) 64 = (−8)�
� = �
13) �� = 1331
� = ��
14) 81 = (−3)�
� = �
15) 100 = ��
� = �
16) 64 = (−2)�
� = �
17) 2401 = ��
� = !
18) �� = −343
� = −!
19) −8 = ��
� = −�
20) �� = 3375
� = �"
21) 1296 = (−6)�
� = �
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Answers
1) �� = 2187
� = �
2) 16 = (−4)�
� = �
3) 256 = ��
� = �
4) 625 = (−5)�
� = �
5) −512 = ��
� = −�
6) �� = 36
� = �
7) −1024 = ��
� = −�
8) �� = 729
� = �
9) 2401 = (−7)�
� = �
10) �� = 64
� = �
11) 27 = 3�
� = �
12) 2197 = ��
� = ��
13) 121 = (−11)�
� = �
14) 225 = ��
� = ��
15) �� = 1296
� = �
16) −1331 = ��
� = −��
17) �� = 1000
� = �
18) 144 = 12�
� = �
19) �� = −125
� = −�
20) 196 = (−14)�
� = �
21) −2197 = ��
� = −��
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Answers
1)�� = − 1512
� = −��
2)34327 = �73��
� = �
3)� 111���
= 121
� = �
4)256 = 2�
� = �
5)729 = ��
� = −����
6) − 64125 = ��
� = −��
7)�� = −512125
� = −��
8) − 8343 = �−2
7��
� = �
9)� 114���
= 196
� = �
10)169 = (−13)�
� = �
11) 1343 = ��
� = �
12) − 216 = ��
� = −!
13)�� = −2764
� = −��
14)64 = (−2)�
� = !
15)�15���
= 625
� = �
16)81 = (−9)�
� = �
17)512 = ��
� = �
18)72964 = ��
� = "�
19)�� = 125216
� = �!
20) 27512 = �38��
� = �
21)�59���
= 8125
� = �
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Answers
1)�� = 1024
� = �
2)6561256 = −94�
�
� = �
3) − 17�
��= − 1
343
� = −�
4)2197 = 13�
� = �
5) − 125 = ��
� = −�
6) 2433125 = ��
� = ��
7)�� = −3375
� = −��
8)12962401 = 67��
� = �
9)10�� = 1000
� = −�
10)729 = 9�
� = �
11) 149 = ��
� = ��
12) − 1331 = ��
� = −��
13)�� = −125216
� = −��
14)1296 = �−6)�
� = �
15) 72���
= 240116
� = −�
16) − 32 = �−2)�
� = �
17) 116 = ��
� = �
18) − 2764 = ��
� = −��
19)�� = 512729
� = !"
20) − 8343 = −2
7��
� = �
21) 45���
= 256625
� = −�
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Solve for x.
Example 1: Example 2:
log4 x = 2
4� = x
log5 25 = x
5� = 25
5� = 5
�x = 2
x = 16
Solve for x.
1) log� 32 = 5
x =
2) log3 x = 3
x =
3) log3 = x
x =
4) log5 = x
x =
181
125
7) log9 x =
x =
8) log� 2 =
x =
1 2
1 3
9) log6 x = 2
x =
10) log4 256 = x
x =
5) log� 36 = 2
x =
6) log2 x = 4
x =
27
–2
8
4
16
2
–4
3
36
6
Answer key
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Solve for x.
Example 1: Example 2:
log4 = x
Solve for x.
2) log6 x = 3
x =x =
1) log� 4 = 2
2
4) log8 = x
x =
164
3) log10 = x
x =
11000
–3
8) log25 x =
x =
1 2
7) log5 x = 2
x = 25
10) log2 x = 8
x =
9) log� 49 = 2
x = 7
6) log� 81 = 4
x =
216
–2
5
256
3
5) log5 625 = x
x = 4
1 16
4� = 1
164
� �4
� =
x = –2
Answer key
log� 81 = 4
x�
= 3�
x = 3
x�
= 81
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Solve for x.
Example 1: Example 2:
log2 = xlog2 x = 3
2� = x
x = 8
Solve for x.
x =
3) log9 = x181
4) log5 x = 3
x =
132
2) log4 x = 2
x =
1) log3 27 = x
x =
8) log� 3 =
x =
1 3
7) log16 x =
x =
1 2
10) log� 64 = 2
x =
9) log7 x = 2
x =
6) log2 = x
x =
125
16
27
8
–5
5) log� 100 = 2
x =
3
–2
4
49
10
1 82
� = 1
82
�̄2
� =
x = –3
Answer key
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Solve for x.
Example 1: Example 2:
log5 x = 2log64 4 = x
64� = 4
4� �
= 4
Solve for x.
5� =
x = 625x = 1 3
12 � 12
5�
= x
1) log4 2 = x 2)
x = x =
log� 64 = 213
3) log6 = x 4) log2 = x16
116
x = x =
5) log = x 6) log� 3 =
x = x =
12
1 8
7) log� 6 = 1 2
x = x =
8) log3 x = 213
9) log4 x = 3 10) log125 25 = x
x = x =
1 2
–1
3
36
64
14
2
–4
729
2 3
81
Logarithmic Equation
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Solve for x.
Example 1: Example 2:
log� 2ˉ2 = –1log81 9 = x
81� = 9
9� �
= 9
Solve for x.
x =
x = 1 2
xˉ1 = � � �4
5) log = x 6) log32 8 = x
x = x =
18
1 4
7) log� 6 = 1 3
x = x =
8) log� 16 = 114
3) log128 = x 4) log4 = x14
12
x = x =
9) log5 x = 3 10) log27 3ˉ2 = x
x = x =
1) 2)
x = x =
log2 x = 215
2 3
216
2 7
–
125
1024
log� 5 =
Answer key
3 5
2
1 2
–
2 3
–
125
1 3
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Solve for x.
Example 1: Example 2:
log25 5�̄ = xlog3
Solve for x.
x =
25� =
� � �5
� �=
� � �
1 3
= �31� �
= � � �� �
=
x = –13 2
–
1) log49 7 = x 2)
x = x =
log� 81 = 212
3) log81 = x 4) log8 = x13
12
x = x =
5) log = x 6) log25 625 = x
x = x =
132
1 2
9) log8 x = 3 10) log� 2ˉ4 = –1
x = x =
7) log� 5 = 1 2
x = x =
8) log7 x = 223
1 2
1 4
–
1 5
512
25
3
1 3
–
16
343
Answer key
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Evaluate each expression.
Example :Evaluate the expression :
log� b� = c log� b
log� a = 1
Answer Answer
Answer Answer
Answer Answer
Answer Answer
Answer Answer
Answer key
.
4) log81 92 log49 7
7) log16 4 – log8 2ˉ31 6
9) log36 6ˉ4 log81 35.
log 2 log64 4 181
13
.log 2 log64 4 = log log64 64181
13
14 181
181
23
.
1 6
=
1) log 6 log81 3 .136
2) log 5 + 4 log32 2125
3) log 3 – log16 12127
5) log125 5 3 log 6.136
6) log32 + 3 log612
136
8) 3 log49 72 log 4116
10) log + 5 log32 21 4164
1 8
– 310
112
– 12
12
– 315
–
1312
3 2
–
5 2
– 4 3
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Evaluate each expression.
Answer key
Example :
log� b� = c log� b
Evaluate the expression : log16 44 + log 3ˉ1
log� a = 1
Answer Answer
Answer Answer
Answer Answer
Answer Answer
Answer Answer
=
1) log 4 – log25 5ˉ21 2
127log16 44 + log 3ˉ1 = log16 162 + log127 127
127
13
13
= 2(1) + (1)
73
1322) log log81 91
4.
164
3) 5 log27 3log 5125
4) log + 6 log8 21 6136
5) log 64 + 7 log125 5 12
6) log 3 – 4 log64 819
7) 3 log 16 log36 6. 14
8) log32 2log 616
9) log81 36 + 2 log 14411210) log128 2 – log 73
149
–3
45
10 3
–
52
–
11 3
–
16
52
5 2
–
1 5
–
2314
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Evaluate each expression.
Example :
log� b� = c log� b
log� a = 1
Answer Answer
Answer Answer
Answer Answer
Answer Answer
Answer Answer
Answer key
1) 2 log27 39 log64 4
.
4) log – 8 log121 1119
181
.5) log 9 log49 716414
6)4 log5 1256 log64 8
7) log – 5 log4 1616
1 36
9) log + 3 log144 121 4917
Evaluate the expression : log128 2ˉ3 – 4 log 125
15
log128 2ˉ3 – 4 log = – log128 128 – log125
15
37
42 125
125
177
–=
3) log 63 + log2 128136
8) log + 9 log4 213
19
10) log – 4 log9 3181
13
2) log 2 5 log3 243132
–8
2 9
112
272
72
–2
–5
4
132
7 4
–
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Solve for x.
Example 1: Example 2:
log4 = 2xlog� � � 27 = 3
(x–1)�
= 27
(x–1)�
= 3�
Solve for x.
2) log3 (x+3) = 4
x =x =
1) log� � 25 = 1
5
4) log4 = x–5
x =
116
3) log7 49 = 2x+6
x = –2
8) log4 (x–9) = 4
x =
7) log5 = 3
x = 250
10) log2 (3x+2) = 5
x =
9) log2� 144 = 2
x = 6
6) log� � � � (729) = 3
x =
78
3
265
10
–4
5) log2 8 = 3x
x = 1
1 16
4� �
= 1 16
4
4� �
=x = –1
Answer key
x–1 = 3
x = 4
x2
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Solve for x.
Example 1: Example 2:
log3 (x–4) = 3
3� = x–4
log5 25 = x+2
5� � �
= 25
5� � �
= 5�
x = 0 x = 31
Solve for x.
1) log� � � (16) = 4
x =
2) log5 5x = 3
x =
3) log6 = x–2
x =
4) log2 = 2x+4
x =
136
164
7) log9 (x–1) =
x =
8) log3� 81 = 4
x =
1 2
9) log7 (x+7) = 2
x =
10) log2 32 = x+9
x =
5) log8� 256 = 2
x =
6) log3 = 3
x =
25
–5
1
–4
108
–5
0
4
42
2
Answer key
27 = x–4
x4
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Solve for x.
Example 1: Example 2:
log8 (2x)� = 2log3
Solve for x.
8� = (2x)
�1 3
= x–5
31� � � � � �
= � � � � � � � �
=
x = 4
1) log36 6 = x+3 2)
x = x =
log3 64 = 2
3) log32 = x–1 4) log3 = 2x14
19
x = x =
5) log = 6) log25 625 = 2x+3
x = x =
132
x 8
9) log9 (x–1) = 3 10) log2 2ˉ4 = 2
x = x =
7) log � � 16 = 4
x = x =
8) log6 (4x) = 212
Answer key
13(8�) = 2x4 = 2xx = 2
15
3 5
730
1
5 2
–
–1
324
8 3
1 2
–
1 8
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Solve for x.
Example 1: Example 2:
log4 4x = 2log64 4 = x+2
(64)� � �
= 44
� � � � = 4
Solve for x.
4� =
x = 64
12 � � � 12
4
= 4x
1) log4 2 = x–5 2)
x = x =
log� � (27) = 3
3) log2 = 2x+1 4) log4 = 14
116
x = x =
5) log = 4x 6) log5� 8 = 3
x = x =
13
19
7) log� � � (16) = 1 2
x = x =
8) log3 (x+4) = 113
9) 2 log4 (x–2) = 4 10) log128 2 = x+3
x = x =
Answer key
x = 5 3
–
3x+6 = 1
x2
112
257
18
3 2
–
1 2
1
–4
23
2 5
207
–
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Solve for x.
Example 1: Example 2:
log2 = 3xlog2 (x+6) = 5
2� = x+6
x = 26
Solve for x.
x =
3) log2 = 5x132
4) log2 = 6
x =
116
2) log10 (x+4) = 2
x =
1) log3 81 = 2x–4
x =
8) log4� 2 =
x =
1 3
7) log3 3x = 4
x =
10) log� � � (243) = 5
x =
9) log6 (x–3) = 2
x =
6) log4 = x+4
x =
128
96
2
–2
–6
5) log� � � (125) = 3
x =
4
–1
27
39
3
1 82
� � = 1
82
�̄2
� � =
x = –1
Answer key
32 = x+6
x2
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Solve for x.
Example 1: Example 2:
log2� 2ˉ4 = –2log49 7 = x+3
(49)� � �
= 7(7
� � � � � = 7
Solve for x.
x = x = –5 2
2xˉ2 = 2ˉ4
2
5) log = x+1 6) log16 8 = 2x+2
x = x =
18
1 2
7) log3� 3 = 14
x = x =
8) log� � � (16) = 212
3) log128 = 4) log2 = 5xx4
18
x = x =
9) log6 (3x–3) = 3 10) log27 3ˉ3 = x–5
x = x =
1) 2)
x = x =
log2 (x–4) =15 log� � � (36) = 2
Answer key
2xˉ2 = (22)ˉ2
17
2 3
27
73
6
8
–
1
3 5
–
5
5 8
–
4
15
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Solve each logarithmic equation.
3) log4 (3x–2) = log4 (x+18)
x =
4) log3 (5x+6) = 2 log3 6
x =
1) log5 (x+7) = log5 (2x+3)
x = 4
2) log2 (x+20) = log2 2
x =
7) log7 (x+1) = log7 (2x+20)
x =
8) log4 (5x–3) = log4 (2x+36)
x =
5) log6 (2x–1) = log6 27
x =
6) log5 24 = log5 (x+2)
x =
11) log5 (2x+2) = log5 (3x+18)
x =
12) log2 (x+17) = 3 log2 2
x =
9) 3 log3 4 = log3 (x+10)
x =
10
–19
14
–16
54
10) log6 4x = log6 100
x =
6
–18
13
22
–9
25
Answer key
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Solve each logarithmic equation.
3) log2 (x+7) = 3 log2 3
x =
4) log5 (3x+7) = log5 (4x+15)
x =
1) log6 2x = log6 68
x =
2) 2 log3 5 = log3 (x+46)
x =
7) log7 (2x+17) = log7 (x+3)
x =
8) log6 (3x–2) = log6 25
x =
5) log4 (7x–3) = log4 (5x+55)
x =
6) log5 48 = log5 (x+4)
x =
11) log3 (1– 4x) = 2 log3 7
x =
12) log4 (3x–15) = log4 (x+67)
x =
9) log2 (x+5) = 4 log2 2
x =
34
20
–14
29
–12
11
10) log5 (x+6) = log5 (2x+24)
x =
–8
–21
9
44
41
–18
Answer key
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Solve each logarithmic equation.
3) log6 5x = log6 75
x =
4) log5 (7x+3) = log5 (8x+32)
x =
1) log2 (x+4) = 2 log2 8
x =
2) log4 (4x–2) = log4 (2x+34)
x =
7) log3 (3–2x) = 2 log3 9
x =
8) log4 (6x–8) = log4 (4x+56)
x =
5) 2 log3 4 = log3 (x+20)
x =
6) log2 (x–2) = 4 log2 3
x =
11) log7 (x+13) = log7 (2x+3)
x =
12) log6 (3x+12) = log6 3
x =
9) log5 74 = log5 (x+6)
x =
60
15
–39
–4
10
68
10) log5 (2x+15) = log5 (3x+37)
x =
–29
18
32
83
–3
–22
Answer key
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Solve each logarithmic equation.
3) log5 (x+5) – log5 2 = log5 50
x =
4) log3 (73+x) = log3 16 + 2 log3 2
x =95 –9
1) log2 (x+3) + log2 (x–3) = log2 91
x =
2) log6 x3+ log6 3 = 4 log6 3
x =10 3
7) log2 6 + log2 (1–x) = 2 log3 6
x =
8) log3 7 = log3 (x+41) – log3 2
x =–5 –27
5) 2 log8 x + log8 2 = log8 72
x =
6) log2 (x–4) – log2 4 = 5 log2 2
x =6 132
9) log4 (x+4) + log4 5 = log4 (3x–2)
x = –11
10) log6 x – log6 3 = 2 log6 5
x = 75
Answer key
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Solve each logarithmic equation.
3) log3 (x–8) = log3 14 + 2 log3 3
x =
4) log5 (2x+4) – log5 4 = log5 28
x =
1) log6 x – log6 4 = 3 log6 4
x =
2) log4 (x+6) + log4 3 = log4 (2x–2)
x =
7) log2 (3–x) + log2 5 = 2 log3 5
x =
8) 3 log8 x + log8 4 = log8 256
x =
5) log3 5 = log3 (x+57) – log3 6
x =
6) log2 (x–1) – log2 9 = 4 log2 2
x =
9) log6 x2+ log6 5 = 3 log6 5
x =
134
256
–2
–27
5
10) log2 (x+16) + log2 3 = log2 6
x =
54
–20
4
145
–14
Answer key
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Solve each logarithmic equation.
3) log2 (5+x) + log2 2 = 3 log3 2
x =
4) log7 (x–5) – log7 4 = 2 log7 5
x =
1) log3 (x–12) = log3 5 + 2 log3 3
x =
2) log2 (x+4) + 3 log2 2 = log2 (6x+4)
x =
7) log6 x – 2 log6 2 = 4 log6 2
x =
8) log2 (x+12) + log2 4 = log2 12
x =
5) log3 12 = log3 (x+16) – log3 5
x =
6) log2 (2–x) + log2 3 = 2 log3 6
x =
9) log4 (x+4) + log4 2 = log4 (3x–7)
x =
–1
57
64
44
15
10) 3 log8 x – log8 7 = log8 49
x =
105
–14
–9
–10
7
Answer key
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� � � � � � � � � �
log7 x+8x+6
= 2
1) 2 log3 x = log3 (12x–36)
x = 6
2) log2 (x–11) + log2 (x–2) = log2 10
x = 12
3)
x = –4
4) log4 (x–5) + log4 (x+5) = log4 24
x = 7
5) 2 log3 (x–1) = log3 3
x = 2
6) 2 log8 x = log8 (7x–12)
x = 4, 3
7) log3 (x+2) + log3 (x–3) = log3 14
x = 5
8) 2 =
x = –3
log4 x+7x+5
Answer key
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� � � � � � � � � �
log7 x+4x+2
= 2
1) log5 (x–7) + log5 (x–5) = –log5 5
x = 7
2) log2 (x+1) + log2 (x–1) = log2 24
x = 5
3) 2 log8 x = log8 (13x –12)
x = 12
4) log4 (x–3) + log4 (x+1) = log4 5
x = 4
5) 2 log3 (x–6) = log3 4
x = 8
6)
x = 0
7) log6 (x+3) + log6 (x–4) = log6 8
x = 5
8) 2 log3 x = log3 (3x–2)
x = 1, 2
Answer key
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� � � � � � � � � �1) log4 (x+3) + log4 (x+3) = log4 49
x =
2)
x =
3) 2 log3 (x–4) = log3 4
x =
4) log3 (13x–42) = 2 log3 x
x =
5) log2 (x–5) + log2 (x–8) = log2 28
x =
6) 2 log8 x = log8 (8–2x)
x =
7) 2 =
x =
4
6
12
–6
8) log5 (x+1) + log5 (x–1) = log5 3
x =
11
6, 7
2
2
log4 x+10x+8
log7 x–36
= log7 3x–10
Answer key