對數之性質

1.已知log2=0.3010

log3=0.4771

則log800

log225各多少?2.設log(1 1/7)

b=log(1 1/49)

試以a

b表示出log2

log73.設log1.4=0.146

log1.8=0.255

log2.1=0.322

求log126=?
1.log800= log(2³ x 10²)= log2³ log10²= 3(log2) 2(log10)= 3 x 0.3010 2 x 1= 2.9030log225= log(3² x 5²)= log3² log5²= 2log3 2log5= 2log3 2log(10/2)= 2log3 2log10 - 2log2= 2 x 0.4771 2 x 1 - 2 x 0.3010= 2.35222.a = log(1 1/7)a = log[(7 1)/7]a = log8 - log7a = log2³ - log73log2 - log7 = a ...... [1]b = log(1 1/49)b = log[(49 1)/49]b = log50 - log49b = log(10²/2) - log7²b = 2log10 - log2 - 2log7log2 2log7 = 2 - b ...... [2][1] x 2 :6log2 - 2log7 = 2a ...... [3][3] [2] :7log2 = 2a - b 2log2 = (2a -b 2)/7[2] x 3 :3log2 6log7 = 6 - 3b ...... [4][4] - [1] :7log7 = 6 - a - 3blog7 =(6 - a - 3b)/73.log1.4 = 0.146log(2 x 7/10) = 0.146log2 log7 - log10 = 0.146log2 log7 = 1.146 ...... [1]log1.8 = 0.255log(2 x 3²/10) = 0.255log2 2log3 - log10 = 0.255log2 2log3 = 1.255 ...... [2]log2.1 = 0.322log(3 x 7/10) = 0.322log3 log7 - log10 = 0.322log3 log7 = 1.322 ...... [3][2] - [1] :2log3 - log7 = 0.109 ...... [4][3] [4] :3log3 = 1.431log3 = 0.477把 log3 = 0.477 代入 [2] 中 :log2 2 x 0.477 = 1.255log2 = 0.301把 log3 = 0.477 代入 [3] 中 :0.477 log7 = 1.322log7 = 0.845log126= log(2 x 3² x 7)= log2 2log3 log7= 0.301 2 x 0.477 0.845= 2.100 參考資料 wanszeto
我先解一題噢 因為想睡覺1. log800可以變成log8 log100 log8 log100=3log2 2log10(因為log8 8為2的3次方 3可以往前移變成3log2 而100為10的2次方2log10 而log10為1)=3x0.3010 2x1=0.903 2=2.903log255=2log15 (225為15的2次方所以2往前提