Exponents - Gwendolyn Brooks College Prepatory Academy · 2015-02-22 · Name : Score : Printable...

Name: __________________________ Score:

Printable Math Worksheets @ www.mathworksheets4kids.com

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

Name: __________________________ Score:



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

Name: __________________________ Score:



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

Name: __________________________ Score:



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

Name: __________________________ Score:



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

Name: __________________________ Score:



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

Name : Score :


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

Name : Score :


Solve for x.


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

Name : Score :


Solve for x.


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

Name : Score :


Solve for x.


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

Name : Score :


Solve for x.


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

Name : Score :


Solve for x.


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

Name : Score :


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

Name : Score :



Example :


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


Name : Score :



Example :


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


Name : Score :


Solve for x.


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

Name : Score :


Solve for x.


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

Name : Score :


Solve for x.


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

Name : Score :


Solve for x.


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

Name : Score :


Solve for x.


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

Name : Score :


Solve for x.


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

Name : Score :


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

Name : Score :



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 =


Name : Score :



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 =


Name : Score :



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 =


Name : Score :



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 =


Name : Score :



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 =


Name : Score :


� � � � � � � � � �

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


Name : Score :


� � � � � � � � � �

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 =


Name : Score :


� � � � � � � � � �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


Name: __________________________ Score:


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

� = �

Name: __________________________ Score:


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 = ��

� = �

Name: __________________________ Score:


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)�

� = �

Name: __________________________ Score:


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 = ��

� = −��

Name: __________________________ Score:


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

� = �

Name: __________________________ Score:


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

� = −�

Name : Score :


Solve for x.


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

Name : Score :


Solve for x.


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

Name : Score :


Solve for x.


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

Name : Score :


Solve for x.


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


Name : Score :


Solve for x.


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

Name : Score :


Solve for x.


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

Name : Score :



Example :Evaluate the expression :


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

Name : Score :



Answer key

Example :


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

Name : Score :



Example :


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

–

Name : Score :


Solve for x.


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

Name : Score :


Solve for x.


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

Name : Score :


Solve for x.


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

Name : Score :


Solve for x.


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

–

Name : Score :


Solve for x.


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

Name : Score :


Solve for x.


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

Name : Score :



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

Name : Score :



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

Name : Score :



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

Name : Score :



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

Name : Score :



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

Name : Score :



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

Name : Score :


� � � � � � � � � �

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

Name : Score :


� � � � � � � � � �

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

Name : Score :


� � � � � � � � � �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

Exponents - Gwendolyn Brooks College Prepatory Academy · 2015-02-22 · Name : Score : Printable...

Documents

Transcript of Exponents - Gwendolyn Brooks College Prepatory Academy · 2015-02-22 · Name : Score : Printable...