Logarithms: Expand, Condense, Properties, Equations - THE "Q"
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Logarithms: Expand, Condense, Properties, Equations
Expand each logarithm.
1) ln (x6 y3)
2) log 8 (x y z3)
( )33 4
3) log 9 7
( )x 3 3
4) log 7 y
5) log 8 (a6b5)
( )u 3 2
7) log 3 v
6) log 4 (63 113)
8) ln 3 u v w
9) log 6 (3 2 56)
10) log 4 (2 11 74)
11) log 6 (c5 3 a)
( )52 5
12) ln 2
( )x 3 6
13) log 5 y
14) log 4 (73 3 2)
15) log 2 (u v w2)
16) log 9 (123 7)6
17) log 9 (c5 3 a)
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Worksheet by Kuta Software LLC
18) log 7 (x5 y)4
( 19) log 7 z2 x )
20) log 8 (u v w5)
Condense each expression to a single logarithm. 21) 2 log 6 u - 8 log 6 v
22) 8 log 5 a + 2 log 5 b
23) 8 log 3 12 + 2 log 3 5
24) 3 log 4 u - 18 log 4 v
25)
2 log 5
z +
log 5 2
x
26) 6 log 2 u - 24 log 2 v
27) 6 log 8 - 30 log 11
28) 4 log 9 11 - 4 log 9 7
29) 3 log x - 5 log y
30) 6 log 6 10 - 24 log 6 3
31) ln z + ln x + ln y 3 3
32) 3 log 4 x + 9 log 4 y
33) 5 log 4 a - 6 log 4 b
34)
log 9
z +
log 9 2
x
+
log 9 2
y
35) 4 log 2 11 - 6 log 2 6
36)
log 7
z +
log 7 3
x
+
log 7 3
y
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Worksheet by Kuta Software LLC
37) 2 log 2 x + 10 log 2 y
38)
log 5
w +
log 5 3
u
+
log 5 3
v
39)
log 3
7 +
log 3 3
10
+
log 3 3
11
40) log 9 u + log 9 v + log 9 w
2
2
2
Rewrite each equation in exponential form. 41) log 17 289 = 2 43) log 14 196 = 2 45) log 100 = 2
1 47) log 6 36 = -2
11
49)
log 27
3
= - 3
2 51) log 64 16 = 3
1 53) log 18 324 = -2
55) log 7 343 = 3
57) log 11 121 = 2 59) log 3 27 = 3
42) log 9 81 = 2
44) log 6 1 = 0
11
46)
log 32
2
= - 5
48) log 18 324 = 2
50) log 2 16 = 4
52) log 7 49 = 2
11
54)
log 81
3
= - 4
1 56) log 225 15 = 2
58) log 14 1 = 0
1 60) log 324 18 = 2
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Worksheet by Kuta Software LLC
Rewrite each equation in logarithmic form. 61) 110 = 1
63) 152 = 225
65) 34 = 81 67) 43 = 64
69) 73 = 343
71) 33 = 27
1
73) 64 2 = 8 75) 162 = 256 77) 192 = 361
79) 12-2 = 1 144
Solve each equation. 81) log 5 26 = log 5 p
83) log 3 (-4x + 7) = log 3 2x 85) log 4 (-4x + 2) = log 4 (-5x - 4)
62) 7-2 = 1 49
1
64)
-
121 2
=
1
11
66) 72 = 49
1
68) 361 2 = 19
70) 11-2 = 1 121
72) 4-2 = 1 16
74) 112 = 121
76) 82 = 64
1
78) 225 2 = 15
1
80) 144 2 = 12
82) log 20 (8 - 2x) = log 20 (-3x + 10) 84) log 4 (x + 6) = log 4 (3x - 6) 86) log 9 3m = log 9 (2m + 3)
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Worksheet by Kuta Software LLC
87) log 19 (-4n - 2) = log 19 (3n + 5) 89) log (-3b + 9) = log (-4b - 10) 91) log 8 (4v - 4) = log 8 (3v - 10) 93) log 2 (-4x - 4) = log 2 (x + 6) 95) log 4 (-2x - 4) = log 4 (3x + 9) 97) log 13 (-5n + 10) = log 13 (10 - n) 99) ln (3n + 9) = ln (-5n + 1) 101) log (5m + 1) = log (m2 - 49) 103) log 17 (-11x - 2) = log 17 (x2 + 26) 105) log 9 (v2 - 87) = log 9 (-v + 3) 107) log 15 (-9n - 1) = log 15 (n2 + 17) 109) log 19 (-12x - 2) = log 19 (x2 + 18) 111) log 18 (-9x + 2) = log 18 (x2 + 16) 113) ln ( p2 - 7) = ln (4 p - 2) 115) log 14 (-24 + 2n2) = log 14 (3n2 + 11n) 117) log 6 (-m2 + 5m) = log 6 (24 - 2m2) 119) log 3 (-20 + 2r2) = log 3 (3r2 + 9r)
88) log 20 (-4n - 5) = log 20 (-3n + 10) 90) log 6 (-5r - 2) = log 6 (r - 4) 92) ln (-2k - 2) = ln (-3k - 9) 94) log 6 3 = log 6 (4 p + 3) 96) ln (-x + 5) = ln (7 - 2x) 98) log 12 (10 - 2a) = log 12 (2a - 6) 100) log 9 (-k + 5) = log 9 (5k - 1) 102) log 8 (r2 + 2r) = log 8 (2 + 3r) 104) log 11 (3b + 2) = log 11 (b2 - 8) 106) ln (3n2 - 5n) = ln (14 + 2n2) 108) log 13 (9a + 2) = log 13 (a2 + 16) 110) log (k2 + 77) = log (-18k - 3) 112) log 17 (-16x + 3) = log 17 (x2 + 63) 114) log 11 -8k = log 11 (20 - k2) 116) log 18 (11x + 3) = log 18 (x2 + 27) 118) log (n2 + 3) = log (5n - 1) 120) log 19 (60 - 2x) = log 19 (x2 - 6x)
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Worksheet by Kuta Software LLC
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