从 Java 1.0 开始，Math 类有了一个自然对数。也就是给定一个参数 x，该自然对数返回 e 的几次幂等于给定的值 x。遗憾的是，Java 语言的(以及 C 、Fortran 和 Basic 的)自然对数函数错误命名为 log()。在我读的每本数学教材中，log 都是以 10 为底的对数，而 ln 是以 e 为底的对数，lg 是以 2 为底的对数。现在已经来不及修复这个问题了，不过 Java 5 添加了一个 log10() 函数，它是以 10 为底而不是以 e 为底的对数。

下面是一个简单程序，它输出整数 1 到 100 的以 2、10 和 e 为底的对数：

1 到 100 的各种底数的对数

Java代码

public class Logarithms {

public static void main(String[] args) {

for (int i = 1; i <= 100; i++) {

System.out.println(i + "\t" +

Math.log10(i) + "\t" +

Math.log(i) + "\t" +

lg(i));

}

}

public static double lg(double x) {

return Math.log(x)/Math.log(2.0);

}

}

C:\ex>javac Logarithms.java

C:\ex>java Logarithms

1 0.0 0.0 0.0

2 0.3010299956639812 0.6931471805599453 1.0

3 0.47712125471966244 1.0986122886681098 1.5849625007211563

4 0.6020599913279624 1.3862943611198906 2.0

5 0.6989700043360189 1.6094379124341003 2.321928094887362

6 0.7781512503836436 1.791759469228055 2.584962500721156

7 0.8450980400142568 1.9459101490553132 2.807354922057604

8 0.9030899869919435 2.0794415416798357 3.0

9 0.9542425094393249 2.1972245773362196 3.1699250014423126

10 1.0 2.302585092994046 3.3219280948873626

11 1.0413926851582251 2.3978952727983707 3.4594316186372978

12 1.0791812460476249 2.4849066497880004 3.5849625007211565

13 1.1139433523068367 2.5649493574615367 3.700439718141092

14 1.146128035678238 2.6390573296152584 3.8073549220576037

15 1.1760912590556813 2.70805020110221 3.9068905956085187

16 1.2041199826559248 2.772588722239781 4.0

17 1.2304489213782739 2.833213344056216 4.08746284125034

18 1.255272505103306 2.8903717578961645 4.169925001442312

19 1.2787536009528289 2.9444389791664403 4.247927513443585

20 1.3010299956639813 2.995732273553991 4.321928094887363

21 1.3222192947339193 3.044522437723423 4.392317422778761

22 1.3424226808222062 3.091042453358316 4.459431618637297

23 1.3617278360175928 3.1354942159291497 4.523561956057013

24 1.380211241711606 3.1780538303479458 4.584962500721157

25 1.3979400086720377 3.2188758248682006 4.643856189774724

26 1.414973347970818 3.258096538021482 4.700439718141093

27 1.4313637641589874 3.295836866004329 4.754887502163469

28 1.4471580313422192 3.332204510175204 4.807354922057604

29 1.462397997898956 3.367295829986474 4.857980995127573

30 1.4771212547196624 3.4011973816621555 4.906890595608519

31 1.4913616938342726 3.4339872044851463 4.954196310386876

32 1.505149978319906 3.4657359027997265 5.0

33 1.5185139398778875 3.4965075614664802 5.044394119358453

34 1.5314789170422551 3.5263605246161616 5.08746284125034

35 1.5440680443502757 3.5553480614894135 5.129283016944966

36 1.5563025007672873 3.58351893845611 5.169925001442312

37 1.568201724066995 3.6109179126442243 5.20945336562895

38 1.5797835966168101 3.6375861597263857 5.247927513443585

39 1.591064607026499 3.6635616461296463 5.285402218862249

40 1.6020599913279623 3.6888794541139363 5.321928094887363

41 1.6127838567197355 3.713572066704308 5.357552004618084

42 1.6232492903979006 3.7376696182833684 5.392317422778761

43 1.6334684555795864 3.7612001156935624 5.426264754702098

44 1.6434526764861874 3.784189633918261 5.459431618637297

45 1.6532125137753437 3.8066624897703196 5.491853096329675

46 1.662757831681574 3.828641396489095 5.523561956057013

47 1.6720978579357175 3.8501476017100584 5.554588851677638

48 1.6812412373755872 3.871201010907891 5.584962500721157

49 1.6901960800285136 3.8918202981106265 5.614709844115208

50 1.6989700043360187 3.912023005428146 5.643856189774724

51 1.7075701760979363 3.9318256327243257 5.672425341971496

52 1.7160033436347992 3.9512437185814275 5.700439718141093

53 1.724275869600789 3.970291913552122 5.7279204545632

54 1.7323937598229686 3.9889840465642745 5.754887502163469

55 1.7403626894942439 4.007333185232471 5.78135971352466

56 1.7481880270062005 4.02535169073515 5.807354922057605

57 1.7558748556724915 4.04305126783455 5.832890014164742

58 1.7634279935629373 4.060443010546419 5.857980995127572

59 1.7708520116421442 4.07753744390572 5.882643049361842

60 1.7781512503836436 4.0943445622221 5.906890595608519

61 1.7853298350107671 4.110873864173311 5.930737337562887

62 1.792391689498254 4.127134385045092 5.954196310386876

63 1.7993405494535817 4.143134726391533 5.977279923499917

64 1.806179973983887 4.1588830833596715 6.0

65 1.8129133566428555 4.174387269895637 6.022367813028454

66 1.8195439355418688 4.189654742026425 6.044394119358453

67 1.8260748027008264 4.204692619390966 6.066089190457772

68 1.8325089127062364 4.219507705176107 6.08746284125034

69 1.8388490907372552 4.23410650459726 6.10852445677817

70 1.845098040014257 4.248495242049359 6.129283016944967

71 1.8512583487190752 4.2626798770413155 6.149747119504682

72 1.8573324964312685 4.276666119016055 6.169925001442312

73 1.863322860120456 4.290459441148391 6.189824558880018

74 1.8692317197309762 4.30406509320417 6.209453365628951

75 1.8750612633917 4.31748811353631 6.22881869049588

76 1.8808135922807914 4.330733340286331 6.247927513443586

77 1.8864907251724818 4.343805421853684 6.266786540694902

78 1.8920946026904804 4.356708826689592 6.285402218862249

79 1.8976270912904414 4.3694478524670215 6.303780748177103

80 1.9030899869919435 4.382026634673881 6.321928094887362

81 1.9084850188786497 4.394449154672439 6.339850002884625

82 1.9138138523837167 4.406719247264253 6.357552004618085

83 1.919078092376074 4.418840607796598 6.375039431346925

84 1.9242792860618816 4.430816798843313 6.39231742277876

85 1.9294189257142926 4.442651256490317 6.409390936137703

86 1.9344984512435677 4.454347296253507 6.426264754702098

87 1.9395192526186185 4.465908118654584 6.442943495848729

88 1.9444826721501687 4.477336814478207 6.459431618637298

89 1.9493900066449128 4.48863636973214 6.475733430966398

90 1.954242509439325 4.499809670330265 6.491853096329675

91 1.9590413923210936 4.51085950651685 6.507794640198696

92 1.9637878273455553 4.5217885770490405 6.523561956057013

93 1.968482948553935 4.532599493153256 6.539158811108032

94 1.9731278535996986 4.543294782270004 6.554588851677638

95 1.9777236052888478 4.553876891600541 6.569855608330948

96 1.9822712330395684 4.564348191467836 6.584962500721156

97 1.9867717342662448 4.574710978503383 6.599912842187128

98 1.9912260756924949 4.584967478670572 6.614709844115209

99 1.99563519459755 4.59511985013459 6.6293566200796095

100 2.0 4.605170185988092 6.643856189774725

public class Logarithms {

public static void main(String[] args) {

for (int i = 1; i <= 100; i++) {

System.out.println(i + "\t" +

Math.log10(i) + "\t" +

Math.log(i) + "\t" +

lg(i));

}

}

public static double lg(double x) {

return Math.log(x)/Math.log(2.0);

}

}

C:\ex>javac Logarithms.java

C:\ex>java Logarithms

1 0.0 0.0 0.0

2 0.3010299956639812 0.6931471805599453 1.0

3 0.47712125471966244 1.0986122886681098 1.5849625007211563

4 0.6020599913279624 1.3862943611198906 2.0

5 0.6989700043360189 1.6094379124341003 2.321928094887362

6 0.7781512503836436 1.791759469228055 2.584962500721156

7 0.8450980400142568 1.9459101490553132 2.807354922057604

8 0.9030899869919435 2.0794415416798357 3.0

9 0.9542425094393249 2.1972245773362196 3.1699250014423126

10 1.0 2.302585092994046 3.3219280948873626

11 1.0413926851582251 2.3978952727983707 3.4594316186372978

12 1.0791812460476249 2.4849066497880004 3.5849625007211565

13 1.1139433523068367 2.5649493574615367 3.700439718141092

14 1.146128035678238 2.6390573296152584 3.8073549220576037

15 1.1760912590556813 2.70805020110221 3.9068905956085187

16 1.2041199826559248 2.772588722239781 4.0

17 1.2304489213782739 2.833213344056216 4.08746284125034

18 1.255272505103306 2.8903717578961645 4.169925001442312

19 1.2787536009528289 2.9444389791664403 4.247927513443585

20 1.3010299956639813 2.995732273553991 4.321928094887363

21 1.3222192947339193 3.044522437723423 4.392317422778761

22 1.3424226808222062 3.091042453358316 4.459431618637297

23 1.3617278360175928 3.1354942159291497 4.523561956057013

24 1.380211241711606 3.1780538303479458 4.584962500721157

25 1.3979400086720377 3.2188758248682006 4.643856189774724

26 1.414973347970818 3.258096538021482 4.700439718141093

27 1.4313637641589874 3.295836866004329 4.754887502163469

28 1.4471580313422192 3.332204510175204 4.807354922057604

29 1.462397997898956 3.367295829986474 4.857980995127573

30 1.4771212547196624 3.4011973816621555 4.906890595608519

31 1.4913616938342726 3.4339872044851463 4.954196310386876

32 1.505149978319906 3.4657359027997265 5.0

33 1.5185139398778875 3.4965075614664802 5.044394119358453

34 1.5314789170422551 3.5263605246161616 5.08746284125034

35 1.5440680443502757 3.5553480614894135 5.129283016944966

36 1.5563025007672873 3.58351893845611 5.169925001442312

37 1.568201724066995 3.6109179126442243 5.20945336562895

38 1.5797835966168101 3.6375861597263857 5.247927513443585

39 1.591064607026499 3.6635616461296463 5.285402218862249

40 1.6020599913279623 3.6888794541139363 5.321928094887363

41 1.6127838567197355 3.713572066704308 5.357552004618084

42 1.6232492903979006 3.7376696182833684 5.392317422778761

43 1.6334684555795864 3.7612001156935624 5.426264754702098

44 1.6434526764861874 3.784189633918261 5.459431618637297

45 1.6532125137753437 3.8066624897703196 5.491853096329675

46 1.662757831681574 3.828641396489095 5.523561956057013

47 1.6720978579357175 3.8501476017100584 5.554588851677638

48 1.6812412373755872 3.871201010907891 5.584962500721157

49 1.6901960800285136 3.8918202981106265 5.614709844115208

50 1.6989700043360187 3.912023005428146 5.643856189774724

51 1.7075701760979363 3.9318256327243257 5.672425341971496

52 1.7160033436347992 3.9512437185814275 5.700439718141093

53 1.724275869600789 3.970291913552122 5.7279204545632

54 1.7323937598229686 3.9889840465642745 5.754887502163469

55 1.7403626894942439 4.007333185232471 5.78135971352466

56 1.7481880270062005 4.02535169073515 5.807354922057605

57 1.7558748556724915 4.04305126783455 5.832890014164742

58 1.7634279935629373 4.060443010546419 5.857980995127572

59 1.7708520116421442 4.07753744390572 5.882643049361842

60 1.7781512503836436 4.0943445622221 5.906890595608519

61 1.7853298350107671 4.110873864173311 5.930737337562887

62 1.792391689498254 4.127134385045092 5.954196310386876

63 1.7993405494535817 4.143134726391533 5.977279923499917

64 1.806179973983887 4.1588830833596715 6.0

65 1.8129133566428555 4.174387269895637 6.022367813028454

66 1.8195439355418688 4.189654742026425 6.044394119358453

67 1.8260748027008264 4.204692619390966 6.066089190457772

68 1.8325089127062364 4.219507705176107 6.08746284125034

69 1.8388490907372552 4.23410650459726 6.10852445677817

70 1.845098040014257 4.248495242049359 6.129283016944967

71 1.8512583487190752 4.2626798770413155 6.149747119504682

72 1.8573324964312685 4.276666119016055 6.169925001442312

73 1.863322860120456 4.290459441148391 6.189824558880018

74 1.8692317197309762 4.30406509320417 6.209453365628951

75 1.8750612633917 4.31748811353631 6.22881869049588

76 1.8808135922807914 4.330733340286331 6.247927513443586

77 1.8864907251724818 4.343805421853684 6.266786540694902

78 1.8920946026904804 4.356708826689592 6.285402218862249

79 1.8976270912904414 4.3694478524670215 6.303780748177103

80 1.9030899869919435 4.382026634673881 6.321928094887362

81 1.9084850188786497 4.394449154672439 6.339850002884625

82 1.9138138523837167 4.406719247264253 6.357552004618085

83 1.919078092376074 4.418840607796598 6.375039431346925

84 1.9242792860618816 4.430816798843313 6.39231742277876

85 1.9294189257142926 4.442651256490317 6.409390936137703

86 1.9344984512435677 4.454347296253507 6.426264754702098

87 1.9395192526186185 4.465908118654584 6.442943495848729

88 1.9444826721501687 4.477336814478207 6.459431618637298

89 1.9493900066449128 4.48863636973214 6.475733430966398

90 1.954242509439325 4.499809670330265 6.491853096329675

91 1.9590413923210936 4.51085950651685 6.507794640198696

92 1.9637878273455553 4.5217885770490405 6.523561956057013

93 1.968482948553935 4.532599493153256 6.539158811108032

94 1.9731278535996986 4.543294782270004 6.554588851677638

95 1.9777236052888478 4.553876891600541 6.569855608330948

96 1.9822712330395684 4.564348191467836 6.584962500721156

97 1.9867717342662448 4.574710978503383 6.599912842187128

98 1.9912260756924949 4.584967478670572 6.614709844115209

99 1.99563519459755 4.59511985013459 6.6293566200796095

100 2.0 4.605170185988092 6.643856189774725

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