求3的100次的第一位数怎么求 已知log 2=0.3010 log 3=0.4771 log7=0.8451
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求3的100次的第一位数怎么求 已知log 2=0.3010 log 3=0.4771 log7=0.8451
![求3的100次的第一位数怎么求 已知log 2=0.3010 log 3=0.4771 log7=0.8451](/uploads/image/z/19029008-56-8.jpg?t=%E6%B1%823%E7%9A%84100%E6%AC%A1%E7%9A%84%E7%AC%AC%E4%B8%80%E4%BD%8D%E6%95%B0%E6%80%8E%E4%B9%88%E6%B1%82+%E5%B7%B2%E7%9F%A5log+2%3D0.3010+log+3%3D0.4771+log7%3D0.8451)
lg5 = lg(10/2) = lg10 - lg2 = 1 - 0.3010 = 0.6990
lg6 = lg(2*3) = lg2 + lg3 = 0.3010 + 0.4771 = 0.7781
lg3^100 = 100lg3 = 100*0.4771 = 47.71
47表示结果有48位数,第一位数应从0.71判断
0.6990< 0.71 < 0.7781
设n = 3^100/(10^47),1≤ n < 10
10 > 1 (10为常用对数的底)
lg5 < lgn < lg6
所以3^100的第一位数是5.
lg6 = lg(2*3) = lg2 + lg3 = 0.3010 + 0.4771 = 0.7781
lg3^100 = 100lg3 = 100*0.4771 = 47.71
47表示结果有48位数,第一位数应从0.71判断
0.6990< 0.71 < 0.7781
设n = 3^100/(10^47),1≤ n < 10
10 > 1 (10为常用对数的底)
lg5 < lgn < lg6
所以3^100的第一位数是5.
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