Name: __________________________
Score:
Exponents
Find the value of x to balance the equation.
1)
= 343
= __________________
4)
729 = 3
= __________________
7)
= 196
2)
1024 = 2
= __________________
5)
225 = = __________________
8)
625 = 3)
512 = = __________________
6)
= 1331
= __________________
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
= __________________
= __________________
= __________________
Printable Math Worksheets @ www.mathworksheets4kids.com
Name: __________________________
Score:
Exponents
Find the value of x to balance the equation.
1)
36 = = __________________
4)
256 = 4
= __________________
7)
2197 = 2)
81 = 3
= __________________
5)
2744 = = __________________
8)
= 100
3)
= 512
= __________________
6)
= 81
= __________________
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 = = __________________
= __________________
= __________________
Printable Math Worksheets @ www.mathworksheets4kids.com
Name: __________________________
Score:
Exponents
Find the value of x to balance the equation.
1)
−1728 = = __________________
4)
= −128
= __________________
7)
125 = 5
2)
= 729
= __________________
5)
225 = (−15)
= __________________
8)
1024 = 3)
256 = (−4)
= __________________
6)
169 = = __________________
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)
= __________________
= __________________
= __________________
Printable Math Worksheets @ www.mathworksheets4kids.com
Name: __________________________
Score:
Exponents
Find the value of x to balance the equation.
1)
= 2187
= __________________
4)
625 = (−5)
= __________________
7)
−1024 = 2)
16 = (−4)
= __________________
5)
−512 = = __________________
8)
= 729
3)
256 = = __________________
6)
= 36
= __________________
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 = = __________________
= __________________
= __________________
Printable Math Worksheets @ www.mathworksheets4kids.com
Name: __________________________
Score:
Exponents
Find the value of x to balance the equation.
1
1) = −
512
343
7 2)
= 27
3
1 3) = 121
11
= __________________
= __________________
4)256 = 2
5)729 = = __________________
64
6) −
= 125
= __________________
= __________________
512
7) = −
125
= __________________
10)169 = (−13)
= __________________
27
13) = −
64
8
2 8) −
= − 343
7
= __________________
= __________________
= __________________
14)64 = (−2
)
= __________________
16)81 = (−9)
17)512 = = __________________
= __________________
19) =
20)
= __________________
1 9) = 196
14
= __________________
1
11)
= 343
= __________________
125
216
= __________________
27
3 = 512
8
= __________________
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12) − 216 = 1 15) = 625
5
= __________________
729
18)
= 64
= __________________
5 81
21) =
9
25
= __________________
Name: __________________________
Score:
Exponents
Find the value of x to balance the equation.
1) = 1024
6561
9 2)
= − 256
4
1 1
3)− = −
7
343
= __________________
= __________________
4)2197 = 13
5) − 125 = = __________________
243
6)
= 3125
= __________________
= __________________
7) = −3375
1296
6 8)
= 2401
7
= __________________
10)729 = 9
= __________________
125
13) = −
216
9)10 = 1000
= __________________
1
11) = 49
= __________________
= __________________
= __________________
14)1296 = −6
)
= __________________
= __________________
16) − 32 = −2)
17)
= __________________
= __________________
19) =
20) −
512
729
= __________________
= __________________
1
= 16
8
2 = − 343
9
= __________________
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12) − 1331 = 2 2401
15) =
7
16
= __________________
27
18) −
= 64
= __________________
4 256
21) =
5
625
= __________________
Name :
Score :
Logarithm - Solve
Solve for x.
Example 1:
log5 25 = x
5 = 25
5 =5
x=2
Example 2:
log4 x = 2
4 =x
x = 16
Solve for x.
1) log 32 = 5
x=
3) log3
x=
1 =x
81
x=
5) log 36 = 2
x=
7) log9 x = 1
2
x=
9) log6 x = 2
x=
2) log3 x = 3
4) log5 1 = x
25
x=
6) log2 x = 4
x=
8) log 2 = 1
3
x=
10) log4 256 = x
x=
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Name :
Score :
Logarithm - Solve
Solve for x.
Example 1:
log 81 = 4
x = 81
x =3
x=3
Example 2:
1
log4 16 = x
4 = 1
16
4 =4
x = –2
Solve for x.
1) log 4 = 2
x=
3) log10
x=
1 =x
1000
x=
5) log5 625 = x
x=
7) log5 x = 2
x=
9) log 49 = 2
x=
2) log6 x = 3
4) log8 1 = x
64
x=
6) log 81 = 4
x=
8) log25 x = 1
2
x=
10) log2 x = 8
x=
Printable Math Worksheets @ www.mathworksheets4kids.com
Name :
Score :
Logarithm - Solve
Solve for x.
Example 1:
log2 x = 3
2 =x
x=8
Example 2:
1
log2 8 = x
2 = 1
8
2 = 2ˉ
x = –3
Solve for x.
1) log3 27 = x
x=
3) log9 1 = x
81
x=
5) log 100 = 2
x=
7) log16 x = 1
2
x=
9) log7 x = 2
x=
2) log4 x = 2
x=
4) log5 x = 3
x=
6) log2 1 = x
32
x=
8) log 3 = 1
3
x=
10) log 64 = 2
x=
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Name :
Score :
Logarithm - Solve
Solve for x.
Example 1:
log64 4 = x
64 = 4
4 =4
1
x= 3
Example 2:
1
log5 x 2 = 2
1
5 = 2
5 =x
x = 625
Solve for x.
1) log4 2 = x
x=
3) log6 1 = x
6
x=
5) log
1 =x
1 8
2
x=
7) log 6 = 1
2
x=
9) log4 x = 3
x=
2) log 64 31 = 2
x=
4) log2 1 = x
16
x=
6) log 3 = 1
4
x=
8) log3 x 31 = 2
x=
10) log125 25 = x
x=
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Name :
Score :
Logarithm - Solve
Solve for x.
Example 1:
log81 9 = x
81 = 9
9 =9
1
x= 2
Example 2:
log 2ˉ2 = –1
xˉ1 =
x =4
Solve for x.
1) log2 x 51 = 2
x=
3) log128 1 = x
4
x=
5) log
1 =x
1 4
8
x=
7) log 6 = 1
3
x=
9) log5 x = 3
x=
2) log 5 = 1
3
x=
4) log4 1 = x
2
x=
6) log32 8 = x
x=
8) log 16 41 = 1
x=
10) log27 3ˉ2 = x
x=
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Name :
Score :
Logarithm - Solve
Solve for x.
Example 1:
log3 1 =
3
= 1
3
=
x = –1
Example 2:
log25 5ˉ = x
25 =
5 =
x=–3
2
Solve for x.
1) log49 7 = x
x=
3) log81 1 = x
3
x=
5) log 1 = x
1
32 2
x=
7) log 5 = 1
2
x=
9) log8 x = 3
x=
1
2) log 812 = 2
x=
4) log8 1 = x
2
x=
6) log25 625 = x
x=
8) log7 x 23 = 2
x=
10) log 2ˉ4 = –1
x=
Printable Math Worksheets @ www.mathworksheets4kids.com
Name :
Score :
Evaluating Expressions
Example :
Evaluate the expression : log
1 . 2 log64 4
181 3
1 . 2 log64 64
log 1 . 2 log64 4 = 1 log
181 3
181 81
4
3
= 1
6
log b = c log b
log a = 1
Evaluate each expression.
1) log 6 . log81 3
361
2) log 5 + 4 log32 2
251
Answer
3) log 3 – log16 1
2
271
Answer
4)
log81 9
2 log49 7
Answer
5) log125 5 . 3 log 6
361
Answer
6) log32 1 + 3 log6 1
2
36
Answer
7)
1
log16 4 – log8 2ˉ3
6
Answer
8) 3 log49 7
2 log 1 4
16
Answer
9) log36 6ˉ4 . log81 35
Answer
10) log
Answer
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1 + 5 log32 2
164 4
Answer
Name :
Score :
Evaluating Expressions
Example :
Evaluate the expression : log16 44 + log 3ˉ1
271
1
log16 44 + log 3ˉ1 = log16 162 + log 1
3
271
271 27
1
= 2(1) + (1)
3
7
= 3
log b = c log b
log a = 1
Evaluate each expression.
1)
1 log 4 – log25 5ˉ2
2
321
2) log 1
4
641
Answer
3) 5 log27 3
log 1 5
25
Answer
4) log 1 + 6 log8 2
6
361
Answer
5) log 64 + 7 log125 5
21
Answer
6) log 3 – 4 log64 8
1
9
Answer
7) 3 log 16 . log36 6
41
Answer
8) log32 2
log 1 6
6
Answer
9) log81 36 + 2 log 144
121
. log81 9
Answer
10) log128 2 – log 73
491
Answer
Printable Math Worksheets @ www.mathworksheets4kids.com
Answer
Name :
Score :
Evaluating Expressions
Example :
Evaluate the expression : log128 2ˉ3 – 4 log 1
251 5
1
log128 2ˉ3 – 4 log 1 = – 3 log128 128 – 4 log
125 25
125 5
7
2
= –17
7
log b = c log b
log a = 1
Evaluate each expression.
1) 2 log27 3
9 log64 4
2) log 1 2 . 5 log3 243
32
Answer
Answer
3) log 63 + log2 128
361
4) log
Answer
5) log
1
1 64
4
. 9 log49 7
Answer
6)
4 log5 125
6 log64 8
Answer
7) log 1 1 – 5 log4 16
6 36
Answer
8) log 1 + 9 log4 2
31 9
Answer
9) log
1 + 3 log144 12
17 49
1 – 8 log121 11
1 81
9
Answer
10) log 1 – 4 log9 3
3
811
Answer
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Answer
Name :
Score :
Logarithm - Solve
Solve for x.
Example 1:
log 27 = 3
(x–1) = 27
(x–1) = 3
x–1 = 3
x=4
Example 2:
1
log4 16 = 2x
4 = 1
16
4 =4
x = –1
Solve for x.
1) log 25 = 1
x=
3) log7 49 = 2x+6
x=
5) log2 8 = 3x
x=
7) log5 x = 3
2
x=
9) log2 144 = 2
x=
2) log3 (x+3) = 4
x=
4) log4 1 = x–5
16
x=
6) log
(729) = 3
x=
8) log4 (x–9) = 4
x=
10) log2 (3x+2) = 5
x=
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Name :
Score :
Logarithm - Solve
Solve for x.
Example 1:
log5 25 = x+2
5 = 25
5 =5
x=0
Example 2:
log3 (x–4) = 3
3 = x–4
27 = x–4
x = 31
Solve for x.
1) log
(16) = 4
x=
x=
3) log6 1 = x–2
36
x=
4) log2 1 = 2x+4
64
x=
5) log8 256 = 2
x=
7) log9 (x–1) = 1
2
x=
9) log7 (x+7) = 2
x=
2) log5 5x = 3
6) log3 x = 3
4
x=
8) log3 81 = 4
x=
10) log2 32 = x+9
x=
Printable Math Worksheets @ www.mathworksheets4kids.com
Name :
Score :
Logarithm - Solve
Solve for x.
Example 1:
log3 1 = x–5
3
= 1
3
=
x = 4
Example 2:
log8 (2x) = 2
8 = (2x)
(8 )31 = 2x
4 = 2x
x=2
Solve for x.
1) log36 6 = x+3
x=
5) log x = 1
1
5
32 8
6) log25 625 = 2x+3
x=
x=
16 = 4
x=
9) log9 (x–1) = 3
x=
4) log3 1 = 2x
9
x=
x=
x=
3) log32 1 = x–1
4
7) log
2) log3 64 = 2
8) log6 (4x) 12 = 2
x=
10) log2 2ˉ4 = 2
x=
Printable Math Worksheets @ www.mathworksheets4kids.com
Name :
Score :
Logarithm - Solve
Solve for x.
Example 1:
log64 4 = x+2
(64) = 4
= 4
4
3x+6 = 1
x= –5
3
Example 2:
1
log4 4x 2 = 2
4 =
4 = 4x
x = 64
Solve for x.
1) log4 2 = x–5
x=
1 = 4x
1 9
3
(16) = 1
2
x=
9) 2 log4 (x–2) = 4
x=
(27) = 3
4) log4 1 = x
16
2
6) log5 8 = 3
x=
x=
x=
x=
7) log
x=
3) log2 1 = 2x+1
4
5) log
2) log
8) log3 (x+4)31 = 1
x=
10) log128 2 = x+3
x=
Printable Math Worksheets @ www.mathworksheets4kids.com
21
Name :
Score :
Logarithm - Solve
Solve for x.
Example 1:
log2 (x+6) = 5
2 = x+6
32 = x+6
x = 26
Example 2:
1
log2 8 = 3x
2 = 1
8
2 = 2ˉ
x = –1
Solve for x.
1) log3 81 = 2x–4
x=
x=
3) log2 1 = 5x
32
x=
5) log
4) log2 x = 6
2
x=
(125) = 3
x=
7) log3 3x = 4
x=
9) log6 (x–3) = 2
x=
2) log10 (x+4) = 2
6) log4 1 = x+4
16
x=
8) log4 2 = 1
3
x=
10) log
x=
Printable Math Worksheets @ www.mathworksheets4kids.com
(243) = 5
Name :
Score :
Logarithm - Solve
Solve for x.
Example 1:
log49 7 = x+3
(49) = 7
(7
=7
x = –5
2
Example 2:
log2 2ˉ4 = –2
2xˉ2 = 2ˉ4
2xˉ2 = (22)ˉ2
x =2
Solve for x.
1) log2 (x–4)51 = 1
5
x=
3) log128 x = 1
7
4
x=
5) log
1 = x+1
1 2
8
x=
7) log3 3 = 1
4
x=
9) log6 (3x–3) = 3
x=
2) log
(36) = 2
x=
4) log2 1 = 5x
8
x=
6) log16 8 = 2x+2
x=
8) log
(16)21 = 2
x=
10) log27 3ˉ3 = x–5
x=
Printable Math Worksheets @ www.mathworksheets4kids.com
Name :
Score :
Logarithmic Equation
Solve each logarithmic equation.
1) log5 (x+7) = log5 (2x+3)
x=
3) log4 (3x–2) = log4 (x+18)
x=
5) log6 (2x–1) = log6 27
x=
7) log7 (x+1) = log7 (2x+20)
x=
9) 3 log3 4 = log3 (x+10)
x=
11) log5 (2x+2) = log5 (3x+18)
x=
2) log2 (x+20) = log2 2
x=
4) log3 (5x+6) = 2 log3 6
x=
6) log5 24 = log5 (x+2)
x=
8) log4 (5x–3) = log4 (2x+36)
x=
10) log6 4x = log6 100
x=
12) log2 (x+17) = 3 log2 2
x=
Printable Math Worksheets @ www.mathworksheets4kids.com
Name :
Score :
Logarithmic Equation
Solve each logarithmic equation.
1) log6 2x = log6 68
x=
3) log2 (x+7) = 3 log2 3
x=
5) log4 (7x–3) = log4 (5x+55)
x=
7) log7 (2x+17) = log7 (x+3)
x=
9) log2 (x+5) = 4 log2 2
x=
11) log3 (1– 4x) = 2 log3 7
x=
2) 2 log3 5 = log3 (x+46)
x=
4) log5 (3x+7) = log5 (4x+15)
x=
6) log5 48 = log5 (x+4)
x=
8) log6 (3x–2) = log6 25
x=
10) log5 (x+6) = log5 (2x+24)
x=
12) log4 (3x–15) = log4 (x+67)
x=
Printable Math Worksheets @ www.mathworksheets4kids.com
Name :
Score :
Logarithmic Equation
Solve each logarithmic equation.
1) log2 (x+4) = 2 log2 8
x=
3) log6 5x = log6 75
x=
5) 2 log3 4 = log3 (x+20)
x=
7) log3 (3–2x) = 2 log3 9
x=
9) log5 74 = log5 (x+6)
x=
11) log7 (x+13) = log7 (2x+3)
x=
2) log4 (4x–2) = log4 (2x+34)
x=
4) log5 (7x+3) = log5 (8x+32)
x=
6) log2 (x–2) = 4 log2 3
x=
8) log4 (6x–8) = log4 (4x+56)
x=
10) log5 (2x+15) = log5 (3x+37)
x=
12) log6 (3x+12) = log6 3
x=
Printable Math Worksheets @ www.mathworksheets4kids.com
Name :
Score :
Logarithmic Equation
Solve each logarithmic equation.
1) log2 (x+3) + log2 (x–3) = log2 91
x=
3) log5 (x+5) – log5 2 = log5 50
x=
5) 2 log8 x + log8 2 = log8 72
x=
7) log2 6 + log2 (1–x) = 2 log3 6
x=
9) log4 (x+4) + log4 5 = log4 (3x–2)
x=
2) log6 x3+ log6 3 = 4 log6 3
x=
4) log3 (73+x) = log3 16 + 2 log3 2
x=
6) log2 (x–4) – log2 4 = 5 log2 2
x=
8) log3 7 = log3 (x+41) – log3 2
x=
10) log6 x – log6 3 = 2 log6 5
x=
Printable Math Worksheets @ www.mathworksheets4kids.com
Name :
Score :
Logarithmic Equation
Solve each logarithmic equation.
1) log6 x – log6 4 = 3 log6 4
x=
3) log3 (x–8) = log3 14 + 2 log3 3
x=
5) log3 5 = log3 (x+57) – log3 6
x=
7) log2 (3–x) + log2 5 = 2 log3 5
x=
9) log6 x2+ log6 5 = 3 log6 5
x=
2) log4 (x+6) + log4 3 = log4 (2x–2)
x=
4) log5 (2x+4) – log5 4 = log5 28
x=
6) log2 (x–1) – log2 9 = 4 log2 2
x=
8) 3 log8 x + log8 4 = log8 256
x=
10) log2 (x+16) + log2 3 = log2 6
x=
Printable Math Worksheets @ www.mathworksheets4kids.com
Name :
Score :
Logarithmic Equation
Solve each logarithmic equation.
1) log3 (x–12) = log3 5 + 2 log3 3
x=
3) log2 (5+x) + log2 2 = 3 log3 2
x=
5) log3 12 = log3 (x+16) – log3 5
x=
7) log6 x – 2 log6 2 = 4 log6 2
x=
9) log4 (x+4) + log4 2 = log4 (3x–7)
x=
2) log2 (x+4) + 3 log2 2 = log2 (6x+4)
x=
4) log7 (x–5) – log7 4 = 2 log7 5
x=
6) log2 (2–x) + log2 3 = 2 log3 6
x=
8) log2 (x+12) + log2 4 = log2 12
x=
10) 3 log8 x – log8 7 = log8 49
x=
Printable Math Worksheets @ www.mathworksheets4kids.com
Name :
Score :
Logarithmic Equation
1) 2 log3 x = log3 (12x–36)
x=
3) log7 x+8 = 2
x+6
x=
5) 2 log3 (x–1) = log3 3
x=
7) log3 (x+2) + log3 (x–3) = log3 14
x=
2) log2 (x–11) + log2 (x–2) = log2 10
x=
4) log4 (x–5) + log4 (x+5) = log4 24
x=
6) 2 log8 x = log8 (7x–12)
x=
8) 2 = log4 x+7
x+5
x=
Printable Math Worksheets @ www.mathworksheets4kids.com
Name :
Score :
Logarithmic Equation
1) log5 (x–7) + log5 (x–5) = –log5 5
x=
3) 2 log8 x = log8 (13x –12)
x=
5) 2 log3 (x–6) = log3 4
x=
7) log6 (x+3) + log6 (x–4) = log6 8
x=
2) log2 (x+1) + log2 (x–1) = log2 24
x=
4) log4 (x–3) + log4 (x+1) = log4 5
x=
6) log7 x+4 = 2
x+2
x=
8) 2 log3 x = log3 (3x–2)
x=
Printable Math Worksheets @ www.mathworksheets4kids.com
Name :
Score :
Logarithmic Equation
1) log4 (x+3) + log4 (x+3) = log4 49
x=
3) 2 log3 (x–4) = log3 4
x=
5) log2 (x–5) + log2 (x–8) = log2 28
x=
7) 2 = log4 x+10
x+8
x=
2) log7 x–3 = log7 3
6
x–10
x=
4) log3 (13x–42) = 2 log3 x
x=
6) 2 log8 x = log8 (8–2x)
x=
8) log5 (x+1) + log5 (x–1) = log5 3
x=
Printable Math Worksheets @ www.mathworksheets4kids.com
Name: __________________________
Score:
Answers
1)
= 343
= 4)
729 = 3
= 7)
= 196
2)
1024 = 2
= 5)
225 = = 8)
625 = 3)
512 = = 6)
= 1331
= 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
= = = Printable Math Worksheets @ www.mathworksheets4kids.com
Name: __________________________
Score:
Answers
1)
36 = = 4)
256 = 4
= 7)
2197 = 2)
81 = 3
= 5)
2744 = = 8)
= 100
3)
= 512
= 6)
= 81
= 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 = = = = Printable Math Worksheets @ www.mathworksheets4kids.com
Name: __________________________
Score:
Answers
1)
−1728 = = −
4)
= −128
= −
7)
125 = 5
2)
= 729
= 5)
225 = (−15)
= 8)
1024 = 3)
256 = (−4)
= 6)
169 = = 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)
= −
= "
= Printable Math Worksheets @ www.mathworksheets4kids.com
Name: __________________________
Score:
Answers
1)
= 2187
= 4)
625 = (−5)
= 7)
−1024 = 2)
16 = (−4)
= 5)
−512 = = −
8)
= 729
3)
256 = = 6)
= 36
= 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 = = −
= = −
Printable Math Worksheets @ www.mathworksheets4kids.com
Name: __________________________
Score:
Answers
1
512
343
7 2)
= 27
3
1 3) = 121
11
= = 4)256 = 2
5)729 = 6) −
= = −
= −
512
7) = −
125
8
2 8) −
= − 343
7
1 9) = 196
14
= = 1) = −
= −
= −
1
= 343
10)169 = (−13)
11)
= =
27
13) = −
64
12) − 216 = 14)64 = (−2
64
= 125
= −!
)
1 15) = 625
5
= !
= 16)81 = (−9)
17)512 = 18)
= = =
125
19) =
216
27
3 20)
= 512
8
5 81
21) =
9
25
= = = −
=
!
Printable Math Worksheets @ www.mathworksheets4kids.com
729
= 64
"
Name: __________________________
Score:
Answers
1) = 1024
6561
9 2)
= − 256
4
1 1
3)− = −
7
343
= = = −
4)2197 = 13
5) − 125 = 6)
= = −
=
7) = −3375
1296
6 8)
= 2401
7
9)10 = 1000
= −
= = −
10)729 = 9
11)
= =
125
13) = −
216
= −
1
= 49
= −
1
= 16
=
!
"
= −
= = =
12) − 1331 = 14)1296 = −6)
17)
512
729
7 2401
15) =
2
16
16) − 32 = −2)
19) =
243
= 3125
18) −
27
= 64
= −
8
2 −
20) −
=
343
7
4 256
21) =
5
625
= = −
Printable Math Worksheets @ www.mathworksheets4kids.com
Name :
Score :
Answer key
Solve for x.
Example 1:
log5 25 = x
5 = 25
5 =5
x=2
Example 2:
log4 x = 2
4 =x
x = 16
Solve for x.
1) log 32 = 5
x=
2
3) log3
1 =x
81
x=
–4
5) log 36 = 2
x=
6
7) log9 x = 1
2
x=
x=
27
4) log5 1 = x
25
x=
–2
6) log2 x = 4
x=
16
8) log 2 = 1
3
3
9) log6 x = 2
x=
2) log3 x = 3
x=
8
10) log4 256 = x
36
x=
Printable Math Worksheets @ www.mathworksheets4kids.com
4
Name :
Score :
Answer key
Solve for x.
Example 1:
log 81 = 4
x = 81
x =3
x=3
Example 2:
1
log4 16 = x
4 = 1
16
4 =4
x = –2
Solve for x.
1) log 4 = 2
x=
3) log10
2) log6 x = 3
2
1 =x
1000
x=
–3
5) log5 625 = x
x=
4
25
9) log 49 = 2
x=
216
4) log8 1 = x
64
x=
–2
6) log 81 = 4
x=
3
8) log25 x = 1
2
7) log5 x = 2
x=
x=
7
x=
5
10) log2 x = 8
x=
Printable Math Worksheets @ www.mathworksheets4kids.com
256
Name :
Score :
Answer key
Solve for x.
Example 1:
log2 x = 3
2 =x
x=8
Example 2:
1
log2 8 = x
2 = 1
8
2 = 2ˉ
x = –3
Solve for x.
1) log3 27 = x
x=
3
3) log9 1 = x
81
x=
–2
5) log 100 = 2
x=
10
7) log16 x = 1
2
x=
4
9) log7 x = 2
x=
2) log4 x = 2
x=
16
4) log5 x = 3
x=
125
6) log2 1 = x
32
x=
–5
8) log 3 = 1
3
x=
27
10) log 64 = 2
49
x=
Printable Math Worksheets @ www.mathworksheets4kids.com
8
Name :
Score :
Logarithmic Equation
Solve for x.
Example 1:
log64 4 = x
64 = 4
4 =4
1
x= 3
Example 2:
1
log5 x 2 = 2
1
5 = 2
5 =x
x = 625
Solve for x.
2) log 64 31 = 2
1) log4 2 = x
1
2
x=
3) log6 1 = x
6
x=
5) log
–1
1 =x
1 8
2
x=
3
7) log 6 = 1
2
x=
36
9) log4 x = 3
x=
x=
2
4) log2 1 = x
16
x=
–4
6) log 3 = 1
4
x=
81
8) log3 x 31 = 2
x=
729
10) log125 25 = x
64
x=
Printable Math Worksheets @ www.mathworksheets4kids.com
2
3
Name :
Score :
Answer key
Solve for x.
Example 1:
log81 9 = x
81 = 9
9 =9
1
x= 2
Example 2:
log 2ˉ2 = –1
xˉ1 =
x =4
Solve for x.
1) log2 x 51 = 2
x=
2) log 5 = 1
3
1024
3) log128 1 = x
4
x=
5) log
–2
7
1 =x
1 4
8
2
3
x=
7) log 6 = 1
3
x=
216
9) log5 x = 3
x=
x=
125
4) log4 1 = x
2
x=
–1
2
6) log32 8 = x
x=
3
5
8) log 16 41 = 1
x=
2
10) log27 3ˉ2 = x
125
x=
Printable Math Worksheets @ www.mathworksheets4kids.com
–2
3
Name :
Score :
Answer key
Solve for x.
Example 1:
log3 1 =
3
= 1
3
=
x = –1
Example 2:
log25 5ˉ = x
25 =
5 =
x=–3
2
Solve for x.
1
2) log 812 = 2
1) log49 7 = x
x=
1
2
3) log81 1 = x
3
x=
–1
4
5) log 1 = x
1
32 2
x=
1
5
7) log 5 = 1
2
x=
25
9) log8 x = 3
x=
x=
3
4) log8 1 = x
2
x=
–1
3
6) log25 625 = x
x=
8) log7 x 23 = 2
x=
343
10) log 2ˉ4 = –1
512
x=
Printable Math Worksheets @ www.mathworksheets4kids.com
16
Name :
Score :
Answer key
Example :
Evaluate the expression : log
1 . 2 log64 4
181 3
1 . 2 log64 64
log 1 . 2 log64 4 = 1 log
181 3
181 81
4
3
= 1
6
log b = c log b
log a = 1
Evaluate each expression.
1) log 6 . log81 3
361
Answer
2) log 5 + 4 log32 2
251
–1
8
3) log 3 – log16 1
2
271
Answer
4)
7)
–1
2
1
2
Answer
–31
5
8) 3 log49 7
2 log 1 4
16
13
12
9) log36 6ˉ4 . log81 35
Answer
Answer
6) log32 1 + 3 log6 1
2
36
1
log16 4 – log8 2ˉ3
6
Answer
3
10
log81 9
2 log49 7
–1
12
5) log125 5 . 3 log 6
361
Answer
Answer
Answer
10) log
–5
2
Printable Math Worksheets @ www.mathworksheets4kids.com
–3
2
1 + 5 log32 2
164 4
Answer
4
3
Name :
Score :
Answer key
Example :
Evaluate the expression : log16 44 + log 3ˉ1
271
1
log16 44 + log 3ˉ1 = log16 162 + log 1
3
271
271 27
1
= 2(1) + (1)
3
7
= 3
log b = c log b
log a = 1
Evaluate each expression.
1)
1 log 4 – log25 5ˉ2
2
321
Answer
4
5
3) 5 log27 3
log 1 5
25
Answer
1
6
Answer
5
2
6) log 3 – 4 log64 8
1
9
–11
3
Answer
–5
2
Answer
–1
5
8) log32 2
log 1 6
6
–3
9) log81 36 + 2 log 144
121
Answer
Answer
–10
3
7) 3 log 16 . log36 6
41
Answer
. log81 9
4) log 1 + 6 log8 2
6
361
5) log 64 + 7 log125 5
21
Answer
2) log 1
4
641
10) log128 2 – log 73
491
–5
2
Printable Math Worksheets @ www.mathworksheets4kids.com
Answer
23
14
Name :
Score :
Answer key
Example :
Evaluate the expression : log128 2ˉ3 – 4 log 1
251 5
1
log128 2ˉ3 – 4 log 1 = – 3 log128 128 – 4 log
125 25
125 5
7
2
= –17
7
log b = c log b
log a = 1
Evaluate each expression.
1) 2 log27 3
9 log64 4
2) log 1 2 . 5 log3 243
32
Answer
2
9
3) log 63 + log2 128
361
Answer
5) log
1
1 64
4
4) log
11
2
. 9 log49 7
Answer
9) log
Answer
–2
4 log5 125
6 log64 8
27
2
Answer
4
8) log 1 + 9 log4 2
31 9
Answer
–8
1 + 3 log144 12
17 49
–5
1 – 8 log121 11
1 81
9
Answer
6)
7) log 1 1 – 5 log4 16
6 36
Answer
Answer
13
2
10) log 1 – 4 log9 3
3
811
7
2
Printable Math Worksheets @ www.mathworksheets4kids.com
Answer
–7
4
Name :
Score :
Answer key
Solve for x.
Example 1:
log 27 = 3
(x–1) = 27
(x–1) = 3
x–1 = 3
x=4
Example 2:
1
log4 16 = 2x
4 = 1
16
4 =4
x = –1
Solve for x.
1) log 25 = 1
x=
5
3) log7 49 = 2x+6
x=
–2
5) log2 8 = 3x
x=
1
250
9) log2 144 = 2
x=
x=
6
78
4) log4 1 = x–5
16
x=
6) log
7) log5 x = 3
2
x=
2) log3 (x+3) = 4
x=
3
(729) = 3
–4
8) log4 (x–9) = 4
x=
265
10) log2 (3x+2) = 5
x=
Printable Math Worksheets @ www.mathworksheets4kids.com
10
Name :
Score :
Answer key
Solve for x.
Example 1:
log5 25 = x+2
5 = 25
5 =5
x=0
Example 2:
log3 (x–4) = 3
3 = x–4
27 = x–4
x = 31
Solve for x.
1) log
x=
(16) = 4
–5
3) log6 1 = x–2
36
x=
0
5) log8 256 = 2
x=
2
7) log9 (x–1) = 1
2
x=
4
9) log7 (x+7) = 2
x=
42
2) log5 5x = 3
x=
25
4) log2 1 = 2x+4
64
x=
–5
6) log3 x = 3
4
x=
108
8) log3 81 = 4
x=
1
10) log2 32 = x+9
x=
Printable Math Worksheets @ www.mathworksheets4kids.com
–4
Name :
Score :
Answer key
Solve for x.
Example 1:
log3 1 = x–5
3
= 1
3
=
x = 4
Example 2:
log8 (2x) = 2
8 = (2x)
(8 )31 = 2x
4 = 2x
x=2
Solve for x.
1) log36 6 = x+3
–5
2
x=
3) log32 1 = x–1
4
3
5
x=
5) log x = 1
1
5
32 8
x=
7) log
x=
16 = 4
1
9) log9 (x–1) = 3
x=
8
3
x=
4) log3 1 = 2x
9
x=
–1
6) log25 625 = 2x+3
–1
2
x=
2) log3 64 = 2
730
8) log6 (4x) 12 = 2
x=
324
10) log2 2ˉ4 = 2
x=
Printable Math Worksheets @ www.mathworksheets4kids.com
1
8
Name :
Score :
Answer key
Solve for x.
Example 1:
log64 4 = x+2
(64) = 4
= 4
4
3x+6 = 1
x= –5
3
Example 2:
1
log4 4x 2 = 2
4 =
4 = 4x
x = 64
Solve for x.
1) log4 2 = x–5
11
2
x=
3) log2 1 = 2x+1
4
–3
2
x=
5) log
1 = 4x
1 9
3
1
2
x=
7) log
x=
(16) = 1
2
257
9) 2 log4 (x–2) = 4
x=
18
2) log
(27) = 3
x=
1
4) log4 1 = x
16
2
x=
–4
6) log5 8 = 3
x=
2
5
8) log3 (x+4)31 = 1
x=
23
10) log128 2 = x+3
x=
Printable Math Worksheets @ www.mathworksheets4kids.com
– 20
7
21
Name :
Score :
Answer key
Solve for x.
Example 1:
log2 (x+6) = 5
2 = x+6
32 = x+6
x = 26
Example 2:
1
log2 8 = 3x
2 = 1
8
2 = 2ˉ
x = –1
Solve for x.
1) log3 81 = 2x–4
x=
4
3) log2 1 = 5x
32
x=
5) log
x=
–1
(125) = 3
3
7) log3 3x = 4
x=
2) log10 (x+4) = 2
x=
4) log2 x = 6
2
6) log4 1 = x+4
16
x=
–6
8) log4 2 = 1
3
x=
9) log6 (x–3) = 2
10) log
39
128
x=
27
x=
96
x=
Printable Math Worksheets @ www.mathworksheets4kids.com
2
(243) = 5
–2
Name :
Score :
Answer key
Solve for x.
Example 1:
log49 7 = x+3
(49) = 7
(7
=7
x = –5
2
Example 2:
log2 2ˉ4 = –2
2xˉ2 = 2ˉ4
2xˉ2 = (22)ˉ2
x =2
Solve for x.
1) log2 (x–4)51 = 1
5
x=
6
3) log128 x = 1
7
4
x=
5) log
8
1 = x+1
1 2
8
x=
–2
3
7) log3 3 = 1
4
x=
27
9) log6 (3x–3) = 3
x=
73
2) log
(36) = 2
x=
5
4) log2 1 = 5x
8
–3
5
x=
6) log16 8 = 2x+2
–5
8
x=
8) log
x=
(16)21 = 2
1
10) log27 3ˉ3 = x–5
x=
Printable Math Worksheets @ www.mathworksheets4kids.com
4
Name :
Score :
Answer key
Solve each logarithmic equation.
1) log5 (x+7) = log5 (2x+3)
x=
4
3) log4 (3x–2) = log4 (x+18)
x=
10
5) log6 (2x–1) = log6 27
x=
14
7) log7 (x+1) = log7 (2x+20)
x=
–19
9) 3 log3 4 = log3 (x+10)
x=
54
11) log5 (2x+2) = log5 (3x+18)
x=
–16
2) log2 (x+20) = log2 2
x=
–18
4) log3 (5x+6) = 2 log3 6
x=
6
6) log5 24 = log5 (x+2)
x=
22
8) log4 (5x–3) = log4 (2x+36)
x=
13
10) log6 4x = log6 100
x=
25
12) log2 (x+17) = 3 log2 2
x=
Printable Math Worksheets @ www.mathworksheets4kids.com
–9
Name :
Score :
Answer key
Solve each logarithmic equation.
1) log6 2x = log6 68
x=
34
3) log2 (x+7) = 3 log2 3
x=
20
5) log4 (7x–3) = log4 (5x+55)
x=
29
7) log7 (2x+17) = log7 (x+3)
x=
–14
9) log2 (x+5) = 4 log2 2
x=
11
11) log3 (1– 4x) = 2 log3 7
x=
–12
2) 2 log3 5 = log3 (x+46)
x=
–21
4) log5 (3x+7) = log5 (4x+15)
x=
–8
6) log5 48 = log5 (x+4)
x=
44
8) log6 (3x–2) = log6 25
x=
9
10) log5 (x+6) = log5 (2x+24)
x=
–18
12) log4 (3x–15) = log4 (x+67)
x=
Printable Math Worksheets @ www.mathworksheets4kids.com
41
Name :
Score :
Answer key
Solve each logarithmic equation.
1) log2 (x+4) = 2 log2 8
x=
60
3) log6 5x = log6 75
x=
15
5) 2 log3 4 = log3 (x+20)
x=
–4
7) log3 (3–2x) = 2 log3 9
x=
–39
9) log5 74 = log5 (x+6)
x=
68
11) log7 (x+13) = log7 (2x+3)
x=
10
2) log4 (4x–2) = log4 (2x+34)
x=
18
4) log5 (7x+3) = log5 (8x+32)
x=
–29
6) log2 (x–2) = 4 log2 3
x=
83
8) log4 (6x–8) = log4 (4x+56)
x=
32
10) log5 (2x+15) = log5 (3x+37)
x=
–22
12) log6 (3x+12) = log6 3
x=
Printable Math Worksheets @ www.mathworksheets4kids.com
–3
Name :
Score :
Answer key
Solve each logarithmic equation.
1) log2 (x+3) + log2 (x–3) = log2 91
x=
10
3) log5 (x+5) – log5 2 = log5 50
x=
95
5) 2 log8 x + log8 2 = log8 72
x=
6
7) log2 6 + log2 (1–x) = 2 log3 6
x=
–5
9) log4 (x+4) + log4 5 = log4 (3x–2)
x=
–11
2) log6 x3+ log6 3 = 4 log6 3
x=
3
4) log3 (73+x) = log3 16 + 2 log3 2
x=
–9
6) log2 (x–4) – log2 4 = 5 log2 2
x=
132
8) log3 7 = log3 (x+41) – log3 2
x=
–27
10) log6 x – log6 3 = 2 log6 5
x=
Printable Math Worksheets @ www.mathworksheets4kids.com
75
Name :
Score :
Answer key
Solve each logarithmic equation.
1) log6 x – log6 4 = 3 log6 4
x=
256
3) log3 (x–8) = log3 14 + 2 log3 3
x=
134
5) log3 5 = log3 (x+57) – log3 6
x=
–27
7) log2 (3–x) + log2 5 = 2 log3 5
x=
–2
9) log6 x2+ log6 5 = 3 log6 5
x=
5
2) log4 (x+6) + log4 3 = log4 (2x–2)
x=
–20
4) log5 (2x+4) – log5 4 = log5 28
x=
54
6) log2 (x–1) – log2 9 = 4 log2 2
x=
145
8) 3 log8 x + log8 4 = log8 256
x=
4
10) log2 (x+16) + log2 3 = log2 6
x=
Printable Math Worksheets @ www.mathworksheets4kids.com
–14
Name :
Score :
Answer key
Solve each logarithmic equation.
1) log3 (x–12) = log3 5 + 2 log3 3
x=
57
3) log2 (5+x) + log2 2 = 3 log3 2
x=
–1
5) log3 12 = log3 (x+16) – log3 5
x=
44
7) log6 x – 2 log6 2 = 4 log6 2
x=
64
9) log4 (x+4) + log4 2 = log4 (3x–7)
x=
15
2) log2 (x+4) + 3 log2 2 = log2 (6x+4)
x=
–14
4) log7 (x–5) – log7 4 = 2 log7 5
x=
105
6) log2 (2–x) + log2 3 = 2 log3 6
x=
–10
8) log2 (x+12) + log2 4 = log2 12
x=
–9
10) 3 log8 x – log8 7 = log8 49
x=
Printable Math Worksheets @ www.mathworksheets4kids.com
7
Name :
Score :
Answer key
1) 2 log3 x = log3 (12x–36)
x=
6
3) log7 x+8 = 2
x+6
x=
–4
5) 2 log3 (x–1) = log3 3
x=
2
7) log3 (x+2) + log3 (x–3) = log3 14
x=
5
2) log2 (x–11) + log2 (x–2) = log2 10
x=
12
4) log4 (x–5) + log4 (x+5) = log4 24
x=
7
6) 2 log8 x = log8 (7x–12)
x=
4, 3
8) 2 = log4 x+7
x+5
x=
Printable Math Worksheets @ www.mathworksheets4kids.com
–3
Name :
Score :
Answer key
1) log5 (x–7) + log5 (x–5) = –log5 5
x=
7
3) 2 log8 x = log8 (13x –12)
x=
12
5) 2 log3 (x–6) = log3 4
x=
8
7) log6 (x+3) + log6 (x–4) = log6 8
x=
5
2) log2 (x+1) + log2 (x–1) = log2 24
x=
5
4) log4 (x–3) + log4 (x+1) = log4 5
x=
4
6) log7 x+4 = 2
x+2
x=
0
8) 2 log3 x = log3 (3x–2)
x=
Printable Math Worksheets @ www.mathworksheets4kids.com
1, 2
Name :
Score :
Answer key
1) log4 (x+3) + log4 (x+3) = log4 49
x=
4
3) 2 log3 (x–4) = log3 4
x=
6
5) log2 (x–5) + log2 (x–8) = log2 28
x=
12
7) 2 = log4 x+10
x+8
x=
–6
2) log7 x–3 = log7 3
6
x–10
x=
11
4) log3 (13x–42) = 2 log3 x
x=
6, 7
6) 2 log8 x = log8 (8–2x)
x=
2
8) log5 (x+1) + log5 (x–1) = log5 3
x=
Printable Math Worksheets @ www.mathworksheets4kids.com
2