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CAPITULO XXXVIII

Logaritmos
Ejercicio 299
Hallar por log el valor de las expresiones siguientes:
  1. 515 × 78.19 6.13 515 × 78.19 6.13 =log( 515 × 78.19 6.13 ) =log(515 × 78.19 ) log6.13 =log515+log78.190.787460 =log515+log78.190.787460 =2.711807+1.8931510.787460 =3.817497968 =antilog( 3.817497968 ) =6568.980424
  2. 23.054 × 934.5 8164 23.054 × 934.5 8164 =log( 23.054 × 934.5 8164 ) =log(23.054 × 934.5 ) log( 8164 ) =log23.054+log934.53.911902996 =1.362746289+2.9705793063.911902996 =0.421422598 =antilog( 0.421422598 ) =2.638897967
  3. 8.14 × 9.73 0.6 × 7.8 8.14 × 9.73 0.6 × 7.8 =log( 8.14 × 9.73 0.6 × 7.8 ) =log(8.14 × 9.73 ) log(0.6 × 7.8 ) =log8.14+log9.73(log0.6+log7.8 ) =0.9106244049+0.9881128403(0.2218487496+0.8920946027 ) =1.228491392 =antilog( 1.228491392 ) =16.92354701
  4. 513.4 × 9.132 85.3 × 10.764 513.4 × 9.132 85.3 × 10.764 =log( 513.4 × 9.132 85.3 × 10.764 ) =log(513.4 × 9.132 ) log(85.3 × 10.764 ) =log513.4+log9.132(log85.3+log10.764 ) =2.710455864+0.9605659028(1.930949031+1.031973689 ) =0.7080990469 =antilog( 0.7080990469 ) =5.10621441
  5. 53.245 × 4325.6 32.815 × 91.79 53.245 × 4325.6 32.815 × 91.79 =log( 53.245 × 4325.6 32.815 × 91.79 ) =log(53.245 × 4325.6 ) log(32.815 × 91.79 ) =log53.245+log4325.6(log32.815+log91.79 ) =1.726278831+3.636046357(1.516072409+1.96279537 ) =1.883457409 =antilog( 1.883457409 ) =76.46406978
  6. 32.6 × (841.9 ) 0.017 × 732.14 Multiplico por 1 32.6 × 841.9 0.017 × 732.14 =log( 32.6 × 841.9 0.017 × 732.14 ) =log(32.6 × 841.9 ) log(0.017 × 732.14 ) =log32.6+log841.9(log0.017+log732.14 ) =1.5132176+2.92526051(1.769551079+2.864594135 ) =3.343435053 =antilog( 3.343435053 ) =2205.134344 32.6 × (841.9 ) 0.017 × 732.14 =2205.134344
  7. 95.36 × (0.14 ) (83.7 ) × ( 2.936 ) 95.36 × 0.14 83.7 × 2.936 =log( 95.36 × 0.14 83.7 × 2.936 ) =log(95.36 × 0.14 ) log(83.7 × 2.936 ) =log95.36+log0.14(log83.7+log2.936 ) =1.9793662420.8538719643(1.922725458+0.4677560512 ) =1.264987231 =antilog(1.264987231 ) =0.0543266304
  8. (7.2 ) × (8.135 ) (0.003 ) × ( 9134.7 ) = 7.2 × 8.135 0.003 × 9134.7 Multiplico por 1 7.2 × 8.135 0.003 × 9134.7 =log( 7.2 × 8.135 0.003 × 9134.7 ) =log(7.2 × 8.135 ) log(0.003 × 9134.7 ) =log7.2+log8.135(log0.003+log9134.7 ) =0.8573324964+0.9103575573(2.522878745+3.960694289 ) =0.3298745101 =antilog( 0.3298745101 ) =2.137344412 (7.2 ) × (8.135 ) (0.003 ) × ( 9134.7 ) =2.137344412
  9. 3 5 × 0. 2 4 3 5 × 0. 2 4 =log( 3 5 × 0. 2 4 ) =log 3 5 +log0. 2 4 =5log3+4log0.2 =5( 0.4771212547 ) +4(0.6989700043 ) =2.3856062742.795880017 =0.4102737437 =antilog(0.4102737437 ) =0.3888
  10. 5 1 2 × 3 2 3 5 1 2 × 3 2 3 =log( 5 1 2 × 3 2 3 ) =log 5 1 2 +log 3 2 3 = 1 2 log5+ 2 3 log3 = 1 2 ( 0.6989700043 ) + 2 3 ( 0.4771212547 ) =0.3494850022+0.3180808365 =0.6675658386 =antilog( 0.6675658386 ) =4.651208827
  11. 2 1 5 × 3 1 2 × 5 3 4 2 1 5 × 3 1 2 × 5 3 4 =log( 2 1 5 × 3 1 2 × 5 3 4 ) =log 2 1 5 +log 3 1 2 +log 5 3 4 = 1 5 log2+ 1 2 log3+ 3 4 log5 = 1 5 ( 0.3010299957 ) + 1 2 ( 0.4771212547 ) + 3 4 ( 0.6989700043 ) =0.06020599913+0.2385606274+0.5242275033 =0.8229941297 =antilog( 0.8229941297 ) =6.652641639
  12. 3 8 5. 6 5 3 8 5. 6 5 =log( 3 8 5. 6 5 ) =log ( 3 ) 8 log ( 5.6 ) 5 =8log35log5.6 =3.8169700383.740940135 =0.07602990273 =antilog( 0.07602990273 ) =1.191324032
  13. 0.5 3 7 2. 5 3 0.5 3 7 2. 5 3 =log( 0.5 3 7 2. 5 3 ) =log ( 0.53 ) 7 log ( 2.5 ) 3 =7log( 0.53 ) 3log( 2.5 ) =1.9300689131.193820026 =3.123888939 =antilog(3.123888939 ) =7.518151 × 1 0 4
  14. 3 2 5 2 5 3 3 2 5 2 5 3 =log( 3 2 5 2 5 3 ) =log 3 2 5 log 2 5 3 = 2 5 log3 5 3 log2 =0.19084850190.5017166594 =0.3108681576 =antilog(0.3108681576 ) =0.4888007262
  15. 7.86 × 8.14 (7.86 × 8.14 ) 1 2 =log (7.86 × 8.14 ) 1 2 = 1 2 log(7.86 × 8.14 ) = 1 2 (log7.86+log8.14 ) = 1 2 (0.895422546+0.9106244049 ) =0.9030234755 =antilog( 0.9030234755 ) =7.998774906
  16. 932.5 × 813.6 × 0.005 (932.5 × 813.6 × 0.005 ) 1 2 =log (932.5 × 813.6 × 0.005 ) 1 2 = 1 2 log(932.5 × 813.6 × 0.005 ) = 1 2 (log932.5+log813.6+log0.005 ) = 1 2 (2.96964884+2.910410942.301029996 ) =1.789514892 =antilog( 1.789514892 ) =61.59066488
  17. 93.7 × 104.2 8.35 × 7.3 ( 93.7 × 104.2 8.35 × 7.3 ) 1 2 =log ( 93.7 × 104.2 8.35 × 7.3 ) 1 2 = 1 2 log( 93.7 × 104.2 8.35 × 7.3 ) = 1 2 [log(93.7 × 104.2 ) log(8.35 × 7.3 ) ] = 1 2 [log93.7+log104.2(log8.35+log7.3 ) ] = 1 2 [1.971739591+2.017867719(0.9216864755+0.8633228601 ) ] =1.102298987 =antilog( 1.102298987 ) =12.65607347
  18. 23.725 × (9.182 ) × 7.184 3 = 23.725 × ( 9.182 ) × 7.184 3 Multiplico por 1 (23.725 × 9.182 × 7.184 ) 1 3 =log (23.725 × 9.182 × 7.184 ) 1 3 = 1 3 log(23.725 × 9.182 × 7.184 ) = 1 3 [log23.725+log9.182+log7.184 ] = 1 3 [1.375206221+0.9629372884+0.8563663237 ] =1.064836611 =antilog( 1.064836611 ) =11.61011739 23.725 × (9.182 ) × 7.184 3 =11.61011739
  19. 12316 × 0.25 931.8 × 0.07 4 ( 12316 × 0.25 931.8 × 0.07 ) 1 4 =log ( 12316 × 0.25 931.8 × 0.07 ) 1 4 = 1 4 log( 12316 × 0.25 931.8 × 0.07 ) = 1 4 [log(12316 × 0.25 ) log(931.8 × 0.07 ) ] = 1 4 [log12316+log0.25(log931.8+log0.07 ) ] = 1 4 [4.090469680.6020599913(2.9693227061.15490196 ) ] =0.4184972357 =antilog( 0.4184972357 ) =2.621182355
  20. 56813 22117 5 ( 56813 22117 ) 1 5 =log ( 56813 22117 ) 1 5 = 1 5 log( 56813 22117 ) = 1 5 [log( 56813 ) log( 22117 ) ] = 1 5 [4.7544477234.344726218 ] =0.08194430096 =antilog( 0.08194430096 ) =1.207658941
  21. ( 0.0316 0.1615 ) 3 2 ( 0.0316 0.1615 ) 3 2 =log ( 0.0316 0.1615 ) 3 2 = 3 2 log( 0.0316 0.1615 ) = 3 2 [log( 0.0316 ) log( 0.1615 ) ] = 3 2 [1.500312917+0.7918274733 ] =1.062728166 =antilog(1.062728166 ) =0.08655094896
  22. 3 3 4 5 2 3 3 3 4 5 2 3 =log( 3 3 4 5 2 3 ) =log ( 3 ) 3 4 log ( 5 ) 2 3 = 3 4 log( 3 ) 2 3 log( 5 ) = 3 4 ( 0.4771212547 ) 2 3 ( 0.6989700043 ) =0.1081390619 =antilog(0.1081390619 ) =0.7795804475
  23. 15 4 7 ( 15 4 ) 1 7 =log ( 15 4 ) 1 7 = 1 7 log( 15 4 ) = 1 7 [log( 15 ) log( 4 ) ] = 1 7 [1.1760912590.6020599913 ] =0.08200446682 =antilog( 0.08200446682 ) =1.207826258
  24. 5 3 5 = 5 3 5 Multiplico por 1 ( 5 3 ) 1 5 =log ( 5 3 ) 1 5 = 1 5 log( 5 3 ) = 1 5 [log( 5 ) log( 3 ) ] = 1 5 [0.69897000430.4771212547 ] =0.04436974992 =antilog( 0.04436974992 ) =1.107566343 5 3 5 =1.107566343
  25. ( 5 8 ) 6 5 ( 5 8 ) 6 5 =log ( 5 8 ) 6 5 = 6 5 log( 5 8 ) = 6 5 [log( 5 ) log( 8 ) ] = 6 5 [0.69897000430.903089987 ] =0.2449439792 =antilog(0.2449439792 ) =0.5689263134
  26. 3 5 × 5 7 3 ( 3 5 ) 1 2 × ( 5 7 ) 1 3 =log[ ( 3 5 ) 1 2 × ( 5 7 ) 1 3 ] =log ( 3 5 ) 1 2 +log ( 5 7 ) 1 3 = 1 2 log( 3 5 ) + 1 3 log( 5 7 ) = 1 2 [log( 3 ) log( 5 ) ] + 1 3 [log( 5 ) log( 7 ) ] = 1 2 [0.47712125470.6989700043 ] + 1 3 [0.69897000430.84509804 ] =0.15963372 =antilog(0.15963372 ) =0.6924147009
  27. 27 × 35 × 0.23 2 1 7 × 3 1 5 × ( 0.2 ) 1 3 =log[ 2 1 7 × 3 1 5 × ( 0.2 ) 1 3 ] =log ( 2 ) 1 7 +log ( 3 ) 1 5 +log ( 0.2 ) 1 3 = 1 7 log( 2 ) + 1 5 log( 3 ) + 1 3 log( 0.2 ) = 1 7 ( 0.3010299957 ) + 1 5 ( 0.4771212547 ) + 1 3 (0.6989700043 ) =0.09456146541 =antilog(0.09456146541 ) =0.8043379031
  28. 32.14 × 59.33 317.64 ( 32.14 ) 1 2 × ( 59.3 ) 1 3 ( 317.6 ) 1 4 =log[ ( 32.14 ) 1 2 × ( 59.3 ) 1 3 ( 317.6 ) 1 4 ] =log( ( 32.14 ) 1 2 × ( 59.3 ) 1 3 ) log ( 317.6 ) 1 4 =log ( 32.14 ) 1 2 +log ( 59.3 ) 1 3 1 4 log( 317.6 ) = 1 2 log( 32.14 ) + 1 3 log( 59.3 ) 1 4 ( 2.501880494 ) = 1 2 ( 1.507045872 ) + 1 3 ( 1.773054693 ) 1 4 ( 2.501880494 ) =0.7190710439 =antilog( 0.7190710439 ) =5.236860966
  29. ( 0.75 ) 2 × 39.162 0.07 × 3.89 ( ( 0.75 ) 2 × 39.162 0.07 × 3.89 ) 1 2 =log ( ( 0.75 ) 2 × 39.162 0.07 × 3.89 ) 1 2 = 1 2 log( ( 0.75 ) 2 × 39.162 0.07 × 3.89 ) = 1 2 [log( ( 0.75 ) 2 × 39.162 ) log(0.07 × 3.89 ) ] = 1 2 [log ( 0.75 ) 2 +log( 39.162 ) (log( 0.07 ) +log( 3.89 ) ) ] = 1 2 [2(0.1249387366 ) +1.592864863(1.15490196+0.5899496013 ) ] =0.9539698743 =antilog( 0.9539698743 ) =8.994351882
  30. ( 0.2 ) 3 × ( 0.3 ) 2 ( 0.05 ) 4 × 3.25 ( ( 0.2 ) 3 × ( 0.3 ) 2 ( 0.05 ) 4 × 3.25 ) 1 2 =log ( ( 0.2 ) 3 × ( 0.3 ) 2 ( 0.05 ) 4 × 3.25 ) 1 2 = 1 2 log( ( 0.2 ) 3 × ( 0.3 ) 2 ( 0.05 ) 4 × 3.25 ) = 1 2 [log( ( 0.2 ) 3 × ( 0.3 ) 2 ) log( ( 0.05 ) 4 × 3.25 ) ] = 1 2 [log ( 0.2 ) 3 +log ( 0.3 ) 2 (log ( 0.05 ) 4 +log( 3.25 ) ) ] = 1 2 [3log( 0.2 ) +2log( 0.3 ) (4log( 0.05 ) +log( 3.25 ) ) ] = 1 2 [3(0.6989700043 ) +2(0.5228787453 ) (4(1.301029996 ) +0.511883361 ) ] =0.7747845591 =antilog( 0.7747845591 ) =5.95366726