java中计算对数

  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

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