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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. 24 = 2 * 2 * 2 * 2 = 16, as well as log 2 (16) = 4
2. 101 is equal to 10, and equivalent to lg (10) = 1.
3. 32 = 3 * 3 = 9, as well as log 3 (9) = 2
4. ln (100) = 4.60517 is equivalent to e4.60517 = 100.
5. ln (e) = 1 is equivalent to e1 = e. 		Some formulas:
 
1. log b (b) = 1, is equivalent to b1 = b. b is real number and represents itself.
2. log b (0) = Unknown, because bunknown = 0.
3. ln (ex) = x.
4. log b (1) = 0, is equivalent to b0 = 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
 
 
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