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CAPITULO XXXVIII

Logaritmos
Ejercicio 300
Dados log 2 = 0.301030, log 3 = 0.477121, log 5 = 0.698970, log 7 = 0.845098
  1. log36 log36 =log( 2 2 × 3 2 ) =log 2 2 +log 3 2 =2log2+2log3 =2( 0.301030 ) +2( 0.477121 ) =0.60206+0.954242 =1.556302
  2. log75 log75 =log(3 × 5 2 ) =log3+log 5 2 =log3+2log5 =0.477121+2( 0.698970 ) =0.477121+1.39794 =1.875061
  3. log30 log30 =log(2 × 3 × 5 ) =log2+log3+log5 =0.301030+0.477121+0.698970 =1.477121
  4. log48 log48 =log( 2 4 × 3 ) =4log2+log3 =4( 0.301030 ) +0.477121 =1.20412+0.477121 =1.681241
  5. log120 log120 =log( 2 3 × 3 × 5 ) =3log2+log3+log5 =3( 0.301030 ) +0.477121+0.698970 =0.90309+1.176091 =2.079181
  6. log98 log98 =log( 7 2 × 2 ) =log 7 2 +log2 =2log7+0.301030 =2( 0.845098 ) +0.301030 =1.690196+0.301030 =1.991226
  7. log0.343 log0.343 =log( 343 1000 ) =log( 7 3 2 3 × 5 3 ) =log ( 7 ) 3 –log( 2 3 × 5 3 ) =3log( 7 ) –(log ( 2 ) 3 +log ( 5 ) 3 ) =3( 0.845098 ) –(3log( 2 ) +3log( 5 ) ) =2.535294–(3( 0.301030 ) +3( 0.698970 ) ) =–0.464706
  8. log22.5 log22.5 =log( 45 2 ) =log( 3 2 × 5 2 ) =log( 3 2 × 5 ) –log2 =log ( 3 ) 2 +log( 5 ) –0.301030 =2log( 3 ) +0.698970–0.301030 =2( 0.477121 ) +0.39794 =1.352182
  9. log1.96 log1.96 =log( 49 25 ) =log( 7 2 5 2 ) =log ( 7 ) 2 –log ( 5 ) 2 =2log( 7 ) –2log( 5 ) =2( 0.845098 ) –2( 0.698970 ) =1.690196–1.39794 =0.292256
  10. log0.875 log0.875 =log( 7 8 ) =log( 7 2 3 ) =log7–log 2 3 =0.845098–3log2 =0.845098–3( 0.301030 ) =0.845098–0.90309 =–0.057992
  11. log202.5 log202.5 =log( 405 2 ) =log( 3 4 × 5 2 ) =log( 3 4 × 5 ) –log2 =log 3 4 +log5–0.301030 =4log3+0.698970–0.301030 =4( 0.477121 ) +0.39794 =1.908484+0.39794 =2.306424
  12. log44.8 log44.8 =log( 224 5 ) =log( 2 5 × 7 5 ) =log( 2 5 × 7 ) –log5 =log 2 5 +log7–0.698970 =5log2+0.845098–0.698970 =5( 0.301030 ) +0.146128 =1.50515+0.146128 =1.651278
  13. log2 1 2 log2 1 2 =log( 5 2 ) =log5–log2 =0.698970–0.301030 =0.39794
  14. log1 1 2 log1 1 2 =log( 3 2 ) =log3–log2 =0.477121–0.301030 =0.176091
  15. log1 2 5 log1 2 5 =log( 7 5 ) =log7–log5 =0.845098–0.698970 =0.146128
  16. log2 1 3 log2 1 3 =log( 7 3 ) =log7–log3 =0.845098–0.477121 =0.367977
  17. Dado log 143 = 2.155336 y log 11 = 1.041393 hallar log 13.
    13 = 143 11 log13 =log( 143 11 ) =log143–log11 =2.155336–1.041393 =1.113943
  18. Dado log 225 = 2.352183 y log 9 = 0.954243 hallar log 25.
    25 = 225 9 log25 =log( 225 9 ) =log225–log9 =2.352183–0.954243 =1.39794
Categories: Capítulo XXXVIII