Kuta Software - Infinite Algebra 1
Name___________________________________
Exponential Functions
Date________________ Period____
Evaluate each function at the given value.
1) f ( x) = x at x
2) f (n) = n at n
3) f (n) = n at n
4) g( x) =
x
6) f ( x)
x
()
at x
Sketch the graph of each function.
5) f ( x) x
()
y
y
x
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-1-
x
Worksheet by Kuta Software LLC
7) f ( x) x
8) f ( x)
()
x
y
x
y
x
Write an equation for each graph.
9)
10)
y
x
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-2-
y
x
Worksheet by Kuta Software LLC
Kuta Software - Infinite Algebra 1
Name___________________________________
Exponential Functions
Date________________ Period____
Evaluate each function at the given value.
1) f ( x) = x at x
2) f (n) = n at n
320
12
3) f (n) = n at n
4) g( x) =
()
x
at x
Sketch the graph of each function.
5) f ( x) x
6) f ( x)
()
y
x
y
x
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-1-
x
Worksheet by Kuta Software LLC
7) f ( x) x
8) f ( x)
()
x
y
x
y
x
Write an equation for each graph.
9)
10)
y
x
y x
()
y
y
x
x
Create your own worksheets like this one with Infinite Algebra 1. Free trial available at KutaSoftware.com
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-2-
Worksheet by Kuta Software LLC
Kuta Software - Infinite Algebra 2
Name___________________________________
The Meaning Of Logarithms
Date________________ Period____
Rewrite each equation in exponential form.
1) log 6 36 = 2
1
= −2
196
3) log 14
2) log 289 17 =
1
2
4) log 3 81 = 4
Rewrite each equation in logarithmic form.
6) 12 2 = 144
1
2
5) 64 = 8
1
81
7) 9 −2 =
( )
1
8)
12
2
=
1
144
Rewrite each equation in exponential form.
15
=v
16
10) log v u = 4
11) log 7 x = y
12) log 2 v = u
9) log u
4
13) log u v = −16
14) log y x = −8
Rewrite each equation in logarithmic form.
15) u
−14
=v
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b
16) 8 = a
-1-
Worksheet by Kuta Software LLC
17)
()
1
5
x
y
=y
19) 9 y = x
18) 6 = x
a
20) b = 123
Evaluate each expression.
21) log 4 64
23) log 4 16
22) log 6 216
24) log 3
1
243
25) log 5 125
26) log 2 4
27) log 343 7
28) log 2 16
29) log 64 4
30) log 6
1
216
Simplify each expression.
31) 12
33) x
log 12 144
log x 72
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32) 5
34) 9
-2-
log 5 17
log 3 20
Worksheet by Kuta Software LLC
Kuta Software - Infinite Algebra 2
Name___________________________________
The Meaning Of Logarithms
Date________________ Period____
Rewrite each equation in exponential form.
1) log 6 36 = 2
2) log 289 17 =
2
1
2
6 = 36
1
2
289 = 17
1
= −2
196
3) log 14
14
−2
=
4) log 3 81 = 4
4
3 = 81
1
196
Rewrite each equation in logarithmic form.
6) 12 2 = 144
1
2
5) 64 = 8
log 64
log 12 144 = 2
1
8=
2
1
81
1
log 9
= −2
81
7) 9 −2 =
( )
1
8)
12
log
2
=
1
12
1
144
1
=2
144
Rewrite each equation in exponential form.
15
=v
16
9) log u
10) log v u = 4
4
v =u
15
uv =
16
11) log 7 x = y
12) log 2 v = u
4
u
()
7
4
2 =v
y
=x
13) log u v = −16
14) log y x = −8
u −16 = v
y −8 = x
Rewrite each equation in logarithmic form.
15) u
−14
=v
b
16) 8 = a
log u v = −14
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log 8 a = b
-1-
Worksheet by Kuta Software LLC
17)
()
1
5
x
y
=y
18) 6 = x
log 6 x = y
log 1 y = x
5
y
19) 9 = x
a
20) b = 123
log 9 x = y
log b 123 = a
Evaluate each expression.
21) log 4 64
22) log 6 216
3
3
23) log 4 16
24) log 3
2
1
243
−5
25) log 5 125
26) log 2 4
3
2
27) log 343 7
28) log 2 16
1
3
4
29) log 64 4
30) log 6
1
3
1
216
−3
Simplify each expression.
31) 12
log 12 144
32) 5
144
33) x
log x 72
log 5 17
17
34) 9
72
log 3 20
400
Create your own worksheets like this one with Infinite Algebra 2. Free trial available at KutaSoftware.com
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-2-
Worksheet by Kuta Software LLC
Kuta Software - Infinite Algebra 2
Name___________________________________
Properties of Logarithms
Date________________ Period____
Expand each logarithm.
1) log (6 ⋅ 11)
5
2) log (5 ⋅ 3)
4) log (3 ⋅ 2 3 )
3) log
( )
5) log
2
5
6) log
x
8) log (a ⋅ b) 2
6
11
4
7) log
y
()
6
6
4
u
9) log
v
11) log
6
5
3
10) log
x⋅ y⋅z
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x
y5
12) log ( x ⋅ y ⋅ z 2 )
-1-
Worksheet by Kuta Software LLC
Condense each expression to a single logarithm.
13) log 3 − log 8
15) 4 log 3 − 4 log 8
17) log 7 − 2 log 12
14)
log 6
3
16) log 2 + log 11 + log 7
18)
2 log 7
3
19) 6 log 3 u + 6 log 3 v
20) ln x − 4 ln y
21) log 4 u − 6 log 4 v
22) log 3 u − 5 log 3 v
23) 20 log 6 u + 5 log 6 v
24) 4 log 3 u − 20 log 3 v
Critical thinking questions:
25) 2(log 2 x − log y) − (log 3 + 2 log 5)
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26) log x ⋅ log 2
-2-
Worksheet by Kuta Software LLC
Kuta Software - Infinite Algebra 2
Name___________________________________
Properties of Logarithms
Date________________ Period____
Expand each logarithm.
1) log (6 ⋅ 11)
2) log (5 ⋅ 3)
log 6 + log 11
3) log
( )
6
11
5
log 5 + log 3
4) log (3 ⋅ 2 3 )
log 3 + 3 log 2
5 log 6 − 5 log 11
4
5) log
2
5
6) log
4 log 2 − log 5
7) log
6
6 log 6 − 6 log 5
8) log (a ⋅ b) 2
x
y
()
6
5
6
2 log a + 2 log b
log x − 6 log y
4
u
9) log
v
10) log
4 log u − log v
11) log
3
x⋅ y⋅z
y5
log x − 5 log y
12) log ( x ⋅ y ⋅ z 2 )
log x log y log z
+
+
3
3
3
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x
log x + log y + 2 log z
-1-
Worksheet by Kuta Software LLC
Condense each expression to a single logarithm.
13) log 3 − log 8
log
3
8
3
log 6
3
log
15) 4 log 3 − 4 log 8
log
14)
3
6
16) log 2 + log 11 + log 7
4
log 154
84
17) log 7 − 2 log 12
18)
7
log
12
3
2
19) 6 log 3 u + 6 log 3 v
log 4
2
20) ln x − 4 ln y
ln
x
y4
22) log 3 u − 5 log 3 v
u
log 3
v6
23) 20 log 6 u + 5 log 6 v
7
log
log 3 (v 6 u 6 )
21) log 4 u − 6 log 4 v
2 log 7
3
u
v5
24) 4 log 3 u − 20 log 3 v
log 6 (v 5 u 20 )
log 3
u4
v
20
Critical thinking questions:
25) 2(log 2 x − log y) − (log 3 + 2 log 5)
log
26) log x ⋅ log 2
4x2
75 y 2
Can't be simplified.
Create your own worksheets like this one with Infinite Algebra 2. Free trial available at KutaSoftware.com
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-2-
Worksheet by Kuta Software LLC
Kuta Software - Infinite Algebra 2
Name___________________________________
Logarithmic Equations
Date________________ Period____
Solve each equation.
1) log 5 x = log (2 x + 9)
2) log (10 − 4 x) = log (10 − 3 x)
3) log (4 p − 2) = log (−5 p + 5)
4) log (4k − 5) = log (2k − 1)
5) log (−2a + 9) = log (7 − 4a)
6) 2 log 7 −2r = 0
7) −10 + log 3 (n + 3) = −10
8) −2 log 5 7 x = 2
9) log −m + 2 = 4
10) −6 log 3 ( x − 3) = −24
11) log 12 (v 2 + 35) = log 12 (−12v − 1)
12) log 9 (−11 x + 2) = log 9 ( x 2 + 30)
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-1-
Worksheet by Kuta Software LLC
13) log (16 + 2b) = log (b 2 − 4b)
14) ln (n 2 + 12) = ln (−9n − 2)
15) log x + log 8 = 2
16) log x − log 2 = 1
17) log 2 + log x = 1
18) log x + log 7 = log 37
19) log 8 2 + log 8 4 x 2 = 1
20) log 9 ( x + 6) − log 9 x = log 9 2
21) log 6 ( x + 1) − log 6 x = log 6 29
22) log 5 6 + log 5 2 x 2 = log 5 48
23) ln 2 − ln (3 x + 2) = 1
24) ln (−3 x − 1) − ln 7 = 2
25) ln ( x − 3) − ln ( x − 5) = ln 5
26) ln (4 x + 1) − ln 3 = 5
©S C2b0U1725 TKruAtGah lSKoofltIwfaSr6eC OLzLtCD.P S AAPlolZ XrMiKgNhQtAsp ar8eusSecrlvnevdT.5 7 RM0aOdaeB Tw8iCtOhe TI0njfDiznuiHtzee FAdl2g9eTbAraaQ W2k.Y
-2-
Worksheet by Kuta Software LLC
Kuta Software - Infinite Algebra 2
Name___________________________________
Logarithmic Equations
Date________________ Period____
Solve each equation.
1) log 5 x = log (2 x + 9)
2) log (10 − 4 x) = log (10 − 3 x)
{3 }
3) log (4 p − 2) = log (−5 p + 5)
{0 }
4) log (4k − 5) = log (2k − 1)
{2 }
{}
7
9
5) log (−2a + 9) = log (7 − 4a)
6) 2 log 7 −2r = 0
{−1}
{ }
−
7) −10 + log 3 (n + 3) = −10
8) −2 log 5 7 x = 2
{−2}
9) log −m + 2 = 4
{ }
1
35
10) −6 log 3 ( x − 3) = −24
{−100}
11) log 12 (v 2 + 35) = log 12 (−12v − 1)
{84}
12) log 9 (−11 x + 2) = log 9 ( x 2 + 30)
{−6}
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1
2
{−7, −4}
-1-
Worksheet by Kuta Software LLC
13) log (16 + 2b) = log (b 2 − 4b)
14) ln (n 2 + 12) = ln (−9n − 2)
{8, −2}
{−2, −7}
15) log x + log 8 = 2
16) log x − log 2 = 1
{20}
{ }
25
2
17) log 2 + log x = 1
18) log x + log 7 = log 37
{5 }
{ }
37
7
19) log 8 2 + log 8 4 x 2 = 1
20) log 9 ( x + 6) − log 9 x = log 9 2
{6 }
{1, −1}
21) log 6 ( x + 1) − log 6 x = log 6 29
22) log 5 6 + log 5 2 x 2 = log 5 48
{2, −2}
{ }
1
28
23) ln 2 − ln (3 x + 2) = 1
{
2 − 2e
3e
24) ln (−3 x − 1) − ln 7 = 2
}
25) ln ( x − 3) − ln ( x − 5) = ln 5
{
−7e 2 − 1
3
}
26) ln (4 x + 1) − ln 3 = 5
{ }
{
11
2
3e 5 − 1
4
}
Create your own worksheets like this one with Infinite Algebra 2. Free trial available at KutaSoftware.com
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-2-
Worksheet by Kuta Software LLC
Kuta Software - Infinite Algebra 2
Name___________________________________
Exponential Equations Not Requiring Logarithms
Date________________ Period____
Solve each equation.
1) 4
2x + 3
=1
2) 5
3 − 2x
3) 3
1 − 2x
= 243
4) 3
2a
=3
5) 4
3x − 2
=1
6) 4
2p
=4
7) 6
−2a
8) 2
2x + 2
=6
2 − 3a
9) 6 3m ⋅ 6 −m = 6 −2m
10)
2x
2
11) 10
−3 x
x
⋅ 10 =
1
10
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=5
−x
−a
−2 p − 1
=2
3x
= 2 −2 x
x
12) 3 −2 x + 1 ⋅ 3 −2 x − 3 = 3 − x
-1-
Worksheet by Kuta Software LLC
13) 4
−2 x
x
15) 2 ⋅
x
⋅ 4 = 64
14) 6
−2 x
18)
81 3n + 2
243
19) 81 ⋅ 9 −2b − 2 = 27
()
r
3x + 2
23) 16 ⋅ 64
⋅ 216
3 − 3r
−x
=
1
216
16) 2 −3 p ⋅ 2 2 p = 2 2 p
1
= 32
32
17) 64 ⋅ 16 −3 x = 16 3 x − 2
1
21)
6
⋅6
3x
= 34
−n
20) 9 −3 x ⋅ 9 x = 27
1
=
216
= 64
©B 82s0C1j2R wKEuEtCat FSJoKfftzwIaLrGeg YLHLgCd.A G sA8lAlc ErfiPgThUtjsz WrxeLsmeJrlvYeTdF.j 6 jMGabdxew PwQiltchl RIanZfcignjistze5 yAvlsgge4b9riak A2i.x
22) 243 k + 2 ⋅ 9 2k − 1 = 9
24) 16
-2-
2p − 3
⋅4
−2 p
=2
4
Worksheet by Kuta Software LLC
Kuta Software - Infinite Algebra 2
Name___________________________________
Exponential Equations Not Requiring Logarithms
Date________________ Period____
Solve each equation.
1) 4
2x + 3
=1
2) 5
3) 3
3
2
1 − 2x
= 243
4) 3
{−2}
5) 4
3x − 2
=1
6) 4
2a
=3
−a
2p
=4
−2 p − 1
{ }
2
3
−2a
−x
{0 }
{}
7) 6
=5
{3 }
{ }
−
3 − 2x
−
=6
2 − 3a
8) 2
{2 }
1
4
2x + 2
=2
3x
{2 }
9) 6 3m ⋅ 6 −m = 6 −2m
10)
2x
2
{0 }
= 2 −2 x
x
{0 }
11) 10
−3 x
x
⋅ 10 =
1
10
12) 3 −2 x + 1 ⋅ 3 −2 x − 3 = 3 − x
{ }
−
{}
1
2
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-1-
2
3
Worksheet by Kuta Software LLC
13) 4
−2 x
x
⋅ 4 = 64
14) 6
−2 x
⋅6
−x
=
{−3}
1
216
{1 }
x
15) 2 ⋅
16) 2 −3 p ⋅ 2 2 p = 2 2 p
1
= 32
32
{0 }
{10}
17) 64 ⋅ 16 −3 x = 16 3 x − 2
18)
81 3n + 2
243
{ }
7
12
{ }
−
19) 81 ⋅ 9 −2b − 2 = 27
{ }
3
4
−
3x + 2
()
{ }
1
21)
6
−
⋅ 216
3x
1
=
216
r
{ }
−
3 − 3r
= 64
3
4
22) 243 k + 2 ⋅ 9 2k − 1 = 9
1
6
23) 16 ⋅ 64
4
17
20) 9 −3 x ⋅ 9 x = 27
{ }
−
= 34
−n
24) 16
2
3
2p − 3
⋅4
−2 p
=2
4
{4 }
{}
6
7
Create your own worksheets like this one with Infinite Algebra 2. Free trial available at KutaSoftware.com
©X U2W0z1623 0KKuNtfaw PSkoTf4ttwFaDrpe4 lLqLnCn.e Y yAFlElJ WrEi4gihetQsB UrzessrePr5v1e6du.5 H oMQaSdIeN cwXiitBhN wIqnrf7iznYigtmeH cALlXg3eKbPrgal D2n.S
-2-
Worksheet by Kuta Software LLC
Kuta Software - Infinite Algebra 2
Name___________________________________
Solving Exponential Equations with Logarithms
Date________________ Period____
Solve each equation. Round your answers to the nearest ten-thousandth.
1) 3 = 17
b
2) 12 = 13
r
n
4) 16 = 67
5) 3 = 69
a
6) 6 = 51
n
7) 6 = 99
8) 20 r = 56
v
3) 9 = 49
9) 5 ⋅ 18
11) 9
6x
n + 10
r
x−1
= 26
10) e
+ 3 = 81
12) 11
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-1-
−5=5
n−8
− 5 = 54
Worksheet by Kuta Software LLC
13) 16
n−7
+ 5 = 24
14) 20
= 20
16) 8
15) 5 ⋅ 6
3m
17) 3.4e
2 − 2n
− 9 = −4
−6n
−5a
18) −6e
+ 6 = 55
− 5 = 53
8n + 8
− 3 = −23
−3.9n − 1
− 1 = −3
19) −e
20) −2e 7v + 5 − 10 = −17
21) −3e 7a + 9 + 6 = −6
22) −3e
23) −e 6 − 9 p + 5 = −48.4
24) −10e 2 − 2b − 6 = −66
25) 6e
−4k − 10
− 4 = 63
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26) 6e
-2-
9x − 1
5x − 6
+ 6 = −58
− 4 = 50
Worksheet by Kuta Software LLC
Kuta Software - Infinite Algebra 2
Name___________________________________
Solving Exponential Equations with Logarithms
Date________________ Period____
Solve each equation. Round your answers to the nearest ten-thousandth.
b
r
1) 3 = 17
2) 12 = 13
2.5789
n
1.0322
v
3) 9 = 49
4) 16 = 67
1.7712
a
1.5165
r
5) 3 = 69
6) 6 = 51
3.854
2.1944
7) 6 n = 99
8) 20 r = 56
2.5646
9) 5 ⋅ 18
6x
= 26
1.3437
10) e
0.0951
11) 9
n + 10
+ 3 = 81
−5=5
3.3026
12) 11
−8.0172
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x−1
n−8
− 5 = 54
9.7005
-1-
Worksheet by Kuta Software LLC
13) 16
n−7
+ 5 = 24
14) 20
8.062
15) 5 ⋅ 6
3m
= 20
16) 8
2 − 2n
− 9 = −4
18) −6e
− 3 = −23
−0.5353
+ 6 = −6
22) −3e
−1.0877
9x − 1
+ 6 = −58
0.4511
23) −e 6 − 9 p + 5 = −48.4
24) −10e 2 − 2b − 6 = −66
0.2247
−4k − 10
8n + 8
20) −2e 7v + 5 − 10 = −17
−0.4341
25) 6e
− 5 = 53
−0.8495
19) −e −3.9n − 1 − 1 = −3
7a + 9
−5a
−0.3905
0.8072
21) −3e
+ 6 = 55
−0.2165
0.2579
17) 3.4e
−6n
0.1041
− 4 = 63
26) 6e
−3.1032
5x − 6
− 4 = 50
1.6394
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-2-
Worksheet by Kuta Software LLC
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