Comparte esto 👍👍DESCARGACAPITULO XXXVIII LogaritmosEjercicio 299Hallar por log el valor de las expresiones siguientes: 515 × 78.19 6.13 515 × 78.19 6.13 =log( 515 × 78.19 6.13 ) =log(515 × 78.19 ) –log6.13 =log515+log78.19–0.787460 =log515+log78.19–0.787460 =2.711807+1.893151–0.787460 =3.817497968 =antilog( 3.817497968 ) =6568.980424 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+log934.5–3.911902996 =1.362746289+2.970579306–3.911902996 =0.421422598 =antilog( 0.421422598 ) =2.638897967 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 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 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 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 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 ) =1.979366242–0.8538719643–(1.922725458+0.4677560512 ) =–1.264987231 =antilog(–1.264987231 ) =0.0543266304 (–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 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 ) =2.385606274–2.795880017 =–0.4102737437 =antilog(–0.4102737437 ) =0.3888 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 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 3 8 5. 6 5 3 8 5. 6 5 =log( 3 8 5. 6 5 ) =log ( 3 ) 8 –log ( 5.6 ) 5 =8log3–5log5.6 =3.816970038–3.740940135 =0.07602990273 =antilog( 0.07602990273 ) =1.191324032 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 ) =–1.930068913–1.193820026 =–3.123888939 =antilog(–3.123888939 ) =7.518151 × 1 0 –4 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 =0.1908485019–0.5017166594 =–0.3108681576 =antilog(–0.3108681576 ) =0.4888007262 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 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+2.91041094–2.301029996 ) =1.789514892 =antilog( 1.789514892 ) =61.59066488 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 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 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 [4.09046968–0.6020599913–(2.969322706–1.15490196 ) ] =0.4184972357 =antilog( 0.4184972357 ) =2.621182355 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 [4.754447723–4.344726218 ] =0.08194430096 =antilog( 0.08194430096 ) =1.207658941 ( 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 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 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 [1.176091259–0.6020599913 ] =0.08200446682 =antilog( 0.08200446682 ) =1.207826258 – 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 [0.6989700043–0.4771212547 ] =0.04436974992 =antilog( 0.04436974992 ) =1.107566343 – 5 3 5 =–1.107566343 ( 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 [0.6989700043–0.903089987 ] =–0.2449439792 =antilog(–0.2449439792 ) =0.5689263134 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 [0.4771212547–0.6989700043 ] + 1 3 [0.6989700043–0.84509804 ] =–0.15963372 =antilog(–0.15963372 ) =0.6924147009 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 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 ( 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 ( 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 Categories: Capítulo XXXVIII