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Logarithm, log calculator. Definition, meaning
Logarithm of
with base
, log
2
4 = 2
What is logarithm?
A logarithm
log
base
( number )
is a numerical object that defines how many times a specific number, called the base, is multiplied by itself to get another number. A logarithm is the opposite, inverse operation to exponentiation. A number of a logarithm is a result of exponentiation. A base of a logarithm is the same as exponentiation power. So exponentiation and logarithm are closely related and complement each other.
There are many kinds of logarithms with some special purpose:
lg
is used, when base is 10. The purpose of the lg is to use it in engineering and science calculations.
ln
is used, when base is e constant. e constant = 2.71828. It is important in mathematics and physics.
Important logarithm is
log2
, because it is related to binary operations (bit operations). It is used in computer science.
Some examples:
1.
2
4
= 2 * 2 * 2 * 2 = 16, as well as
log
2
(16)
= 4
2.
10
1
is equal to 10, and equivalent to
lg (10) = 1
.
3.
3
2
= 3 * 3 = 9, as well as
log
3
(9)
= 2
4.
ln (100)
= 4.60517 is equivalent to
e
4.60517
= 100.
5.
ln (e)
= 1 is equivalent to
e
1
= e.
Some formulas:
1.
log
b
(b)
= 1, is equivalent to b
1
= b. b is real number and represents itself.
2.
log
b
(0)
= Unknown, because b
unknown
= 0.
3.
ln (e
x
)
= x.
4.
log
b
(1)
= 0, is equivalent to
b
0
= 1. b is real number
Set of logarithms with base 2
log
2
1
= 0
log
2
26
= 4.700439718
log
2
51
= 5.672425342
log
2
76
= 6.247927513
log
2
2
= 1
log
2
27
= 4.754887502
log
2
52
= 5.700439718
log
2
77
= 6.266786541
log
2
3
= 1.584962501
log
2
28
= 4.807354922
log
2
53
= 5.727920455
log
2
78
= 6.285402219
log
2
4
= 2
log
2
29
= 4.857980995
log
2
54
= 5.754887502
log
2
79
= 6.303780748
log
2
5
= 2.321928095
log
2
30
= 4.906890596
log
2
55
= 5.781359714
log
2
80
= 6.321928095
log
2
6
= 2.584962501
log
2
31
= 4.95419631
log
2
56
= 5.807354922
log
2
81
= 6.339850003
log
2
7
= 2.807354922
log
2
32
= 5
log
2
57
= 5.832890014
log
2
82
= 6.357552005
log
2
8
= 3
log
2
33
= 5.044394119
log
2
58
= 5.857980995
log
2
83
= 6.375039431
log
2
9
= 3.169925001
log
2
34
= 5.087462841
log
2
59
= 5.882643049
log
2
84
= 6.392317423
log
2
10
= 3.321928095
log
2
35
= 5.129283017
log
2
60
= 5.906890596
log
2
85
= 6.409390936
log
2
11
= 3.459431619
log
2
36
= 5.169925001
log
2
61
= 5.930737338
log
2
86
= 6.426264755
log
2
12
= 3.584962501
log
2
37
= 5.209453366
log
2
62
= 5.95419631
log
2
87
= 6.442943496
log
2
13
= 3.700439718
log
2
38
= 5.247927513
log
2
63
= 5.977279923
log
2
88
= 6.459431619
log
2
14
= 3.807354922
log
2
39
= 5.285402219
log
2
64
= 6
log
2
89
= 6.475733431
log
2
15
= 3.906890596
log
2
40
= 5.321928095
log
2
65
= 6.022367813
log
2
90
= 6.491853096
log
2
16
= 4
log
2
41
= 5.357552005
log
2
66
= 6.044394119
log
2
91
= 6.50779464
log
2
17
= 4.087462841
log
2
42
= 5.392317423
log
2
67
= 6.06608919
log
2
92
= 6.523561956
log
2
18
= 4.169925001
log
2
43
= 5.426264755
log
2
68
= 6.087462841
log
2
93
= 6.539158811
log
2
19
= 4.247927513
log
2
44
= 5.459431619
log
2
69
= 6.108524457
log
2
94
= 6.554588852
log
2
20
= 4.321928095
log
2
45
= 5.491853096
log
2
70
= 6.129283017
log
2
95
= 6.569855608
log
2
21
= 4.392317423
log
2
46
= 5.523561956
log
2
71
= 6.14974712
log
2
96
= 6.584962501
log
2
22
= 4.459431619
log
2
47
= 5.554588852
log
2
72
= 6.169925001
log
2
97
= 6.599912842
log
2
23
= 4.523561956
log
2
48
= 5.584962501
log
2
73
= 6.189824559
log
2
98
= 6.614709844
log
2
24
= 4.584962501
log
2
49
= 5.614709844
log
2
74
= 6.209453366
log
2
99
= 6.62935662
log
2
25
= 4.64385619
log
2
50
= 5.64385619
log
2
75
= 6.22881869
log
2
100
= 6.64385619
Logarithms of number 4
log
1
4
= NAN
log
26
4
= 0.425492107
log
51
4
= 0.352582869
log
76
4
= 0.320106147
log
2
4
= 2
log
27
4
= 0.420619836
log
52
4
= 0.350850127
log
77
4
= 0.319142831
log
3
4
= 1.261859507
log
28
4
= 0.416029195
log
53
4
= 0.34916686
log
78
4
= 0.318197616
log
4
4
= 1
log
29
4
= 0.411693665
log
54
4
= 0.347530686
log
79
4
= 0.317269918
log
5
4
= 0.861353116
log
30
4
= 0.407590094
log
55
4
= 0.345939381
log
80
4
= 0.316359182
log
6
4
= 0.773705614
log
31
4
= 0.403698173
log
56
4
= 0.344390868
log
81
4
= 0.315464877
log
7
4
= 0.712414374
log
32
4
= 0.4
log
57
4
= 0.342883201
log
82
4
= 0.314586495
log
8
4
= 0.666666667
log
33
4
= 0.396479726
log
58
4
= 0.341414559
log
83
4
= 0.31372355
log
9
4
= 0.630929754
log
34
4
= 0.393123264
log
59
4
= 0.339983233
log
84
4
= 0.312875577
log
10
4
= 0.602059991
log
35
4
= 0.389918044
log
60
4
= 0.338587615
log
85
4
= 0.31204213
log
11
4
= 0.578129653
log
36
4
= 0.386852807
log
61
4
= 0.337226197
log
86
4
= 0.311222783
log
12
4
= 0.557885891
log
37
4
= 0.38391744
log
62
4
= 0.335897558
log
87
4
= 0.310417126
log
13
4
= 0.540476309
log
38
4
= 0.381102825
log
63
4
= 0.334600358
log
88
4
= 0.309624765
log
14
4
= 0.52529907
log
39
4
= 0.378400719
log
64
4
= 0.333333333
log
89
4
= 0.308845326
log
15
4
= 0.51191605
log
40
4
= 0.375803649
log
65
4
= 0.332095292
log
90
4
= 0.308078444
log
16
4
= 0.5
log
41
4
= 0.373304822
log
66
4
= 0.330885108
log
91
4
= 0.307323773
log
17
4
= 0.489301084
log
42
4
= 0.370898047
log
67
4
= 0.329701713
log
92
4
= 0.306580977
log
18
4
= 0.479624933
log
43
4
= 0.368577666
log
68
4
= 0.3285441
log
93
4
= 0.305849737
log
19
4
= 0.470817827
log
44
4
= 0.366338502
log
69
4
= 0.327411311
log
94
4
= 0.305129741
log
20
4
= 0.462756426
log
45
4
= 0.364175801
log
70
4
= 0.326302439
log
95
4
= 0.304420693
log
21
4
= 0.455340497
log
46
4
= 0.362085194
log
71
4
= 0.325216625
log
96
4
= 0.303722307
log
22
4
= 0.448487648
log
47
4
= 0.360062653
log
72
4
= 0.324153049
log
97
4
= 0.303034305
log
23
4
= 0.442129459
log
48
4
= 0.358104464
log
73
4
= 0.323110935
log
98
4
= 0.302356422
log
24
4
= 0.436208584
log
49
4
= 0.356207187
log
74
4
= 0.322089544
log
99
4
= 0.301688401
log
25
4
= 0.430676558
log
50
4
= 0.35436764
log
75
4
= 0.321088171
log
100
4
= 0.301029996
