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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. 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