Common logarithm (base 10)
This is a table of common (base-10) logarithms.
After the table is the program that generated
the table.
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x log(x)
1 0
1.001 0.00043408
1.002 0.00086772
1.003 0.00130093
1.004 0.00173371
1.005 0.00216606
1.006 0.00259798
1.007 0.00302947
1.008 0.00346053
1.009 0.00389117
1.01 0.00432137
1.011 0.00475116
1.012 0.00518051
1.013 0.00560945
1.014 0.00603795
1.015 0.00646604
1.016 0.00689371
1.017 0.00732095
1.018 0.00774778
1.019 0.00817418
1.02 0.00860017
1.021 0.00902574
1.022 0.0094509
1.023 0.00987563
1.024 0.01029996
1.025 0.01072387
1.026 0.01114736
1.027 0.01157044
1.028 0.01199311
1.029 0.01241537
1.03 0.01283722
1.031 0.01325867
1.032 0.0136797
1.033 0.01410032
1.034 0.01452054
1.035 0.01494035
1.036 0.01535976
1.037 0.01577876
1.038 0.01619735
1.039 0.01661555
1.04 0.01703334
1.041 0.01745073
1.042 0.01786772
1.043 0.01828431
1.044 0.0187005
1.045 0.01911629
1.046 0.01953168
1.047 0.01994668
1.048 0.02036128
1.049 0.02077549
1.05 0.0211893
1.051 0.02160272
1.052 0.02201574
1.053 0.02242837
1.054 0.02284061
1.055 0.02325246
1.056 0.02366392
1.057 0.02407499
1.058 0.02448567
1.059 0.02489596
1.06 0.02530587
1.061 0.02571538
1.062 0.02612452
1.063 0.02653326
1.064 0.02694163
1.065 0.02734961
1.066 0.0277572
1.067 0.02816442
1.068 0.02857125
1.069 0.02897771
1.07 0.02938378
1.071 0.02978947
1.072 0.03019479
1.073 0.03059972
1.074 0.03100428
1.075 0.03140846
1.076 0.03181227
1.077 0.0322157
1.078 0.03261876
1.079 0.03302144
1.08 0.03342376
1.081 0.03382569
1.082 0.03422726
1.083 0.03462846
1.084 0.03502928
1.085 0.03542974
1.086 0.03582983
1.087 0.03622954
1.088 0.0366289
1.089 0.03702788
1.09 0.0374265
1.091 0.03782475
1.092 0.03822264
1.093 0.03862016
1.094 0.03901732
1.095 0.03941412
1.096 0.03981055
1.097 0.04020663
1.098 0.04060234
1.099 0.04099769
1.1 0.04139269
1.101 0.04178732
1.102 0.04218159
1.103 0.04257551
1.104 0.04296907
1.105 0.04336228
1.106 0.04375513
1.107 0.04414762
1.108 0.04453976
1.109 0.04493155
1.11 0.04532298
1.111 0.04571406
1.112 0.04610479
1.113 0.04649516
1.114 0.04688519
1.115 0.04727487
1.116 0.04766419
1.117 0.04805317
1.118 0.0484418
1.119 0.04883009
1.12 0.04921802
1.121 0.04960561
1.122 0.04999286
1.123 0.05037976
1.124 0.05076631
1.125 0.05115252
1.126 0.05153839
1.127 0.05192392
1.128 0.0523091
1.129 0.05269394
1.13 0.05307844
1.131 0.0534626
1.132 0.05384643
1.133 0.05422991
1.134 0.05461305
1.135 0.05499586
1.136 0.05537833
1.137 0.05576046
1.138 0.05614226
1.139 0.05652372
1.14 0.05690485
1.141 0.05728564
1.142 0.0576661
1.143 0.05804623
1.144 0.05842602
1.145 0.05880549
1.146 0.05918462
1.147 0.05956342
1.148 0.05994189
1.149 0.06032003
1.15 0.06069784
1.151 0.06107532
1.152 0.06145248
1.153 0.06182931
1.154 0.06220581
1.155 0.06258198
1.156 0.06295783
1.157 0.06333336
1.158 0.06370856
1.159 0.06408344
1.16 0.06445799
1.161 0.06483222
1.162 0.06520613
1.163 0.06557971
1.164 0.06595298
1.165 0.06632593
1.166 0.06669855
1.167 0.06707086
1.168 0.06744284
1.169 0.06781451
1.17 0.06818586
1.171 0.0685569
1.172 0.06892761
1.173 0.06929801
1.174 0.0696681
1.175 0.07003787
1.176 0.07040732
1.177 0.07077646
1.178 0.07114529
1.179 0.07151381
1.18 0.07188201
1.181 0.0722499
1.182 0.07261748
1.183 0.07298474
1.184 0.0733517
1.185 0.07371835
1.186 0.07408469
1.187 0.07445072
1.188 0.07481644
1.189 0.07518185
1.19 0.07554696
1.191 0.07591176
1.192 0.07627626
1.193 0.07664044
1.194 0.07700433
1.195 0.07736791
1.196 0.07773118
1.197 0.07809415
1.198 0.07845682
1.199 0.07881918
1.2 0.07918125
1.201 0.07954301
1.202 0.07990447
1.203 0.08026563
1.204 0.08062649
1.205 0.08098705
1.206 0.08134731
1.207 0.08170727
1.208 0.08206693
1.209 0.0824263
1.21 0.08278537
1.211 0.08314414
1.212 0.08350262
1.213 0.0838608
1.214 0.08421869
1.215 0.08457628
1.216 0.08493357
1.217 0.08529058
1.218 0.08564729
1.219 0.08600371
1.22 0.08635983
1.221 0.08671566
1.222 0.08707121
1.223 0.08742646
1.224 0.08778142
1.225 0.08813609
1.226 0.08849047
1.227 0.08884456
1.228 0.08919837
1.229 0.08955188
1.23 0.08990511
1.231 0.09025805
1.232 0.09061071
1.233 0.09096308
1.234 0.09131516
1.235 0.09166696
1.236 0.09201847
1.237 0.0923697
1.238 0.09272064
1.239 0.09307131
1.24 0.09342169
1.241 0.09377178
1.242 0.0941216
1.243 0.09447113
1.244 0.09482038
1.245 0.09516935
1.246 0.09551804
1.247 0.09586645
1.248 0.09621459
1.249 0.09656244
1.25 0.09691001
1.251 0.09725731
1.252 0.09760433
1.253 0.09795107
1.254 0.09829754
1.255 0.09864373
1.256 0.09898964
1.257 0.09933528
1.258 0.09968064
1.259 0.10002573
1.26 0.10037055
1.261 0.10071509
1.262 0.10105935
1.263 0.10140335
1.264 0.10174707
1.265 0.10209053
1.266 0.10243371
1.267 0.10277661
1.268 0.10311925
1.269 0.10346162
1.27 0.10380372
1.271 0.10414555
1.272 0.10448711
1.273 0.1048284
1.274 0.10516943
1.275 0.10551018
1.276 0.10585067
1.277 0.1061909
1.278 0.10653085
1.279 0.10687054
1.28 0.10720997
1.281 0.10754913
1.282 0.10788803
1.283 0.10822666
1.284 0.10856502
1.285 0.10890313
1.286 0.10924097
1.287 0.10957855
1.288 0.10991586
1.289 0.11025292
1.29 0.11058971
1.291 0.11092624
1.292 0.11126251
1.293 0.11159852
1.294 0.11193428
1.295 0.11226977
1.296 0.112605
1.297 0.11293998
1.298 0.11327469
1.299 0.11360915
1.3 0.11394335
1.301 0.1142773
1.302 0.11461098
1.303 0.11494442
1.304 0.11527759
1.305 0.11561051
1.306 0.11594318
1.307 0.11627559
1.308 0.11660774
1.309 0.11693965
1.31 0.1172713
1.311 0.11760269
1.312 0.11793384
1.313 0.11826473
1.314 0.11859537
1.315 0.11892575
1.316 0.11925589
1.317 0.11958577
1.318 0.11991541
1.319 0.1202448
1.32 0.12057393
1.321 0.12090282
1.322 0.12123146
1.323 0.12155984
1.324 0.12188799
1.325 0.12221588
1.326 0.12254352
1.327 0.12287092
1.328 0.12319808
1.329 0.12352498
1.33 0.12385164
1.331 0.12417806
1.332 0.12450422
1.333 0.12483015
1.334 0.12515583
1.335 0.12548127
1.336 0.12580646
1.337 0.12613141
1.338 0.12645611
1.339 0.12678058
1.34 0.1271048
1.341 0.12742878
1.342 0.12775252
1.343 0.12807601
1.344 0.12839927
1.345 0.12872228
1.346 0.12904506
1.347 0.1293676
1.348 0.12968989
1.349 0.13001195
1.35 0.13033377
1.351 0.13065535
1.352 0.13097669
1.353 0.1312978
1.354 0.13161866
1.355 0.1319393
1.356 0.13225969
1.357 0.13257985
1.358 0.13289977
1.359 0.13321946
1.36 0.13353891
1.361 0.13385813
1.362 0.13417711
1.363 0.13449586
1.364 0.13481437
1.365 0.13513265
1.366 0.1354507
1.367 0.13576851
1.368 0.1360861
1.369 0.13640345
1.37 0.13672057
1.371 0.13703745
1.372 0.13735411
1.373 0.13767054
1.374 0.13798673
1.375 0.1383027
1.376 0.13861843
1.377 0.13893394
1.378 0.13924922
1.379 0.13956427
1.38 0.13987909
1.381 0.14019368
1.382 0.14050804
1.383 0.14082218
1.384 0.14113609
1.385 0.14144977
1.386 0.14176323
1.387 0.14207646
1.388 0.14238947
1.389 0.14270225
1.39 0.1430148
1.391 0.14332713
1.392 0.14363924
1.393 0.14395112
1.394 0.14426277
1.395 0.14457421
1.396 0.14488542
1.397 0.14519641
1.398 0.14550717
1.399 0.14581771
1.4 0.14612804
1.401 0.14643814
1.402 0.14674801
1.403 0.14705767
1.404 0.14736711
1.405 0.14767632
1.406 0.14798532
1.407 0.1482941
1.408 0.14860265
1.409 0.14891099
1.41 0.14921911
1.411 0.14952701
1.412 0.1498347
1.413 0.15014216
1.414 0.15044941
1.415 0.15075644
1.416 0.15106325
1.417 0.15136985
1.418 0.15167623
1.419 0.1519824
1.42 0.15228834
1.421 0.15259408
1.422 0.1528996
1.423 0.1532049
1.424 0.15350999
1.425 0.15381486
1.426 0.15411953
1.427 0.15442397
1.428 0.15472821
1.429 0.15503223
1.43 0.15533604
1.431 0.15563963
1.432 0.15594302
1.433 0.15624619
1.434 0.15654915
1.435 0.1568519
1.436 0.15715444
1.437 0.15745677
1.438 0.15775889
1.439 0.15806079
1.44 0.15836249
1.441 0.15866398
1.442 0.15896526
1.443 0.15926633
1.444 0.15956719
1.445 0.15986785
1.446 0.16016829
1.447 0.16046853
1.448 0.16076856
1.449 0.16106839
1.45 0.161368
1.451 0.16166741
1.452 0.16196662
1.453 0.16226561
1.454 0.16256441
1.455 0.16286299
1.456 0.16316138
1.457 0.16345955
1.458 0.16375752
1.459 0.16405529
1.46 0.16435286
1.461 0.16465022
1.462 0.16494737
1.463 0.16524433
1.464 0.16554108
1.465 0.16583762
1.466 0.16613397
1.467 0.16643011
1.468 0.16672606
1.469 0.1670218
1.47 0.16731733
1.471 0.16761267
1.472 0.16790781
1.473 0.16820275
1.474 0.16849748
1.475 0.16879202
1.476 0.16908636
1.477 0.1693805
1.478 0.16967443
1.479 0.16996817
1.48 0.17026172
1.481 0.17055506
1.482 0.1708482
1.483 0.17114115
1.484 0.1714339
1.485 0.17172645
1.486 0.17201881
1.487 0.17231097
1.488 0.17260293
1.489 0.1728947
1.49 0.17318627
1.491 0.17347764
1.492 0.17376882
1.493 0.17405981
1.494 0.1743506
1.495 0.17464119
1.496 0.17493159
1.497 0.1752218
1.498 0.17551181
1.499 0.17580163
1.5 0.17609126
1.501 0.17638069
1.502 0.17666993
1.503 0.17695898
1.504 0.17724784
1.505 0.1775365
1.506 0.17782497
1.507 0.17811325
1.508 0.17840134
1.509 0.17868924
1.51 0.17897695
1.511 0.17926446
1.512 0.17955179
1.513 0.17983893
1.514 0.18012588
1.515 0.18041263
1.516 0.1806992
1.517 0.18098558
1.518 0.18127177
1.519 0.18155777
1.52 0.18184359
1.521 0.18212921
1.522 0.18241465
1.523 0.1826999
1.524 0.18298497
1.525 0.18326984
1.526 0.18355453
1.527 0.18383904
1.528 0.18412335
1.529 0.18440749
1.53 0.18469143
1.531 0.18497519
1.532 0.18525877
1.533 0.18554215
1.534 0.18582536
1.535 0.18610838
1.536 0.18639122
1.537 0.18667387
1.538 0.18695634
1.539 0.18723862
1.54 0.18752072
1.541 0.18780264
1.542 0.18808437
1.543 0.18836593
1.544 0.1886473
1.545 0.18892848
1.546 0.18920949
1.547 0.18949031
1.548 0.18977096
1.549 0.19005142
1.55 0.1903317
1.551 0.1906118
1.552 0.19089172
1.553 0.19117146
1.554 0.19145101
1.555 0.19173039
1.556 0.19200959
1.557 0.19228861
1.558 0.19256745
1.559 0.19284612
1.56 0.1931246
1.561 0.1934029
1.562 0.19368103
1.563 0.19395898
1.564 0.19423675
1.565 0.19451434
1.566 0.19479176
1.567 0.195069
1.568 0.19534606
1.569 0.19562294
1.57 0.19589965
1.571 0.19617619
1.572 0.19645254
1.573 0.19672872
1.574 0.19700473
1.575 0.19728056
1.576 0.19755621
1.577 0.19783169
1.578 0.198107
1.579 0.19838213
1.58 0.19865709
1.581 0.19893187
1.582 0.19920648
1.583 0.19948091
1.584 0.19975518
1.585 0.20002927
1.586 0.20030318
1.587 0.20057693
1.588 0.2008505
1.589 0.2011239
1.59 0.20139712
1.591 0.20167018
1.592 0.20194306
1.593 0.20221578
1.594 0.20248832
1.595 0.20276069
1.596 0.20303289
1.597 0.20330492
1.598 0.20357678
1.599 0.20384846
1.6 0.20411998
1.601 0.20439133
1.602 0.20466251
1.603 0.20493352
1.604 0.20520436
1.605 0.20547504
1.606 0.20574554
1.607 0.20601588
1.608 0.20628604
1.609 0.20655604
1.61 0.20682588
1.611 0.20709554
1.612 0.20736504
1.613 0.20763437
1.614 0.20790353
1.615 0.20817253
1.616 0.20844136
1.617 0.20871002
1.618 0.20897852
1.619 0.20924685
1.62 0.20951501
1.621 0.20978301
1.622 0.21005085
1.623 0.21031852
1.624 0.21058602
1.625 0.21085337
1.626 0.21112054
1.627 0.21138755
1.628 0.2116544
1.629 0.21192108
1.63 0.2121876
1.631 0.21245396
1.632 0.21272015
1.633 0.21298618
1.634 0.21325205
1.635 0.21351776
1.636 0.2137833
1.637 0.21404868
1.638 0.2143139
1.639 0.21457895
1.64 0.21484385
1.641 0.21510858
1.642 0.21537315
1.643 0.21563756
1.644 0.21590181
1.645 0.2161659
1.646 0.21642983
1.647 0.2166936
1.648 0.21695721
1.649 0.21722066
1.65 0.21748394
1.651 0.21774707
1.652 0.21801004
1.653 0.21827285
1.654 0.21853551
1.655 0.218798
1.656 0.21906033
1.657 0.21932251
1.658 0.21958453
1.659 0.21984639
1.66 0.22010809
1.661 0.22036963
1.662 0.22063102
1.663 0.22089225
1.664 0.22115332
1.665 0.22141424
1.666 0.221675
1.667 0.2219356
1.668 0.22219605
1.669 0.22245634
1.67 0.22271647
1.671 0.22297645
1.672 0.22323627
1.673 0.22349594
1.674 0.22375545
1.675 0.22401481
1.676 0.22427401
1.677 0.22453306
1.678 0.22479196
1.679 0.2250507
1.68 0.22530928
1.681 0.22556771
1.682 0.22582599
1.683 0.22608412
1.684 0.22634209
1.685 0.22659991
1.686 0.22685757
1.687 0.22711508
1.688 0.22737244
1.689 0.22762965
1.69 0.2278867
1.691 0.22814361
1.692 0.22840036
1.693 0.22865696
1.694 0.22891341
1.695 0.2291697
1.696 0.22942585
1.697 0.22968184
1.698 0.22993769
1.699 0.23019338
1.7 0.23044892
1.701 0.23070431
1.702 0.23095956
1.703 0.23121465
1.704 0.23146959
1.705 0.23172438
1.706 0.23197903
1.707 0.23223352
1.708 0.23248787
1.709 0.23274206
1.71 0.23299611
1.711 0.23325001
1.712 0.23350376
1.713 0.23375736
1.714 0.23401082
1.715 0.23426412
1.716 0.23451728
1.717 0.2347703
1.718 0.23502316
1.719 0.23527588
1.72 0.23552845
1.721 0.23578087
1.722 0.23603315
1.723 0.23628528
1.724 0.23653726
1.725 0.2367891
1.726 0.23704079
1.727 0.23729234
1.728 0.23754374
1.729 0.23779499
1.73 0.2380461
1.731 0.23829707
1.732 0.23854789
1.733 0.23879856
1.734 0.23904909
1.735 0.23929948
1.736 0.23954972
1.737 0.23979982
1.738 0.24004977
1.739 0.24029958
1.74 0.24054925
1.741 0.24079877
1.742 0.24104815
1.743 0.24129739
1.744 0.24154648
1.745 0.24179543
1.746 0.24204424
1.747 0.24229291
1.748 0.24254143
1.749 0.24278981
1.75 0.24303805
1.751 0.24328615
1.752 0.2435341
1.753 0.24378192
1.754 0.24402959
1.755 0.24427712
1.756 0.24452451
1.757 0.24477176
1.758 0.24501887
1.759 0.24526584
1.76 0.24551267
1.761 0.24575936
1.762 0.2460059
1.763 0.24625231
1.764 0.24649858
1.765 0.24674471
1.766 0.2469907
1.767 0.24723655
1.768 0.24748226
1.769 0.24772783
1.77 0.24797327
1.771 0.24821856
1.772 0.24846372
1.773 0.24870874
1.774 0.24895362
1.775 0.24919836
1.776 0.24944296
1.777 0.24968743
1.778 0.24993176
1.779 0.25017595
1.78 0.25042
1.781 0.25066392
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9.998 0.99991313
9.999 0.99995657
10 1
Here is the Java program that uses a
Taylor series to calculate the natural
(base-e) logarithm, and then multiplies to
convert this value to the base-10 logarithm.
(Note: A Taylor series is a calculus topic.)
import java.io.*;
import java.text.*;
public class logtab {
/*method*/ public static void main(String args[]) {
try {
DecimalFormat df=new DecimalFormat("###.########");
DataOutput f2=new DataOutputStream(new FileOutputStream(args[0]));
f2.writeBytes(" x log(x)\r\n");
double x=1.0;
double dx=0.001;
double dx2=dx*dx;
double dx3=dx2*dx;
double dx4=dx3*dx;
double dx5=dx4*dx;
double dx6=dx5*dx;
double dx7=dx6*dx;
double nlog=0.0; /*natural logarithm*/
for (int i=1; i<=9001; i++) {
double x2=x*x;
double x3=x2*x;
double x4=x3*x;
double x5=x4*x;
double x6=x5*x;
double x7=x6*x;
double log10=nlog*0.434294482; /*convert natural logarithm
to base 10 logarithm*/
String xs=df.format(x);
if (xs.length()==1) {xs+=" ";}
else if (xs.length()==2) {xs+=" ";}
else if (xs.length()==3) {xs+=" ";}
else if (xs.length()==4) {xs+=" ";}
/*output*/
f2.writeBytes(xs+" "+df.format(log10)+"\r\n");
if ((i%10)==0) f2.writeBytes(" \r\n");
/*natural logarithm approximation using Taylor series*/
nlog+=dx/x-dx2/(2*x2)+dx3/(3*x3)-dx4/(4*x4)+dx5/(5*x5)
-dx6/(6*x6)+dx7/(7*x7);
x+=dx;
} /*end i loop*/
} catch (Exception ex) {String err=ex.toString();
System.out.print(err);}
} /*end main*/
} /*end logtab*/