- 346 名前：１３２人目の素数さん mailto:sage [2011/05/04(水) 11:11:36.85 ]
- >>338 (中)
>>344
e = 2.71828183 は使っていい？
3^(1/3) ≦ e^(1/e),
の対数をとって
log(3) ≦ 3/e = 1.10363832 (1.09861229)
〔解1〕
(3/2)^3 = 3*(9/8) = 3*{1 + 1/(2^3)},
3log(3/2) = log(3) + log(9/8) ≦ 3/e + 1/(2^3),
log(3/2) ≦ 1/e + 1/(3*2^3) = 0.4095461
〔解2〕
(3/2)^8 = (3^3)(243/256) = (3^3){1 - 13/(2^8)},
8log(3/2) = 3log(3) + log(243/256) ≦ 9/e - 13/(2^8),
log(3/2) ≦ (9/8e) - 13/(8*2^8) = 0.4075167
〔解3〕
(3/2)^19 = (3^7)(531441/524288) = (3^7){1 + 7153/(2^19)},
19log(3/2) = 7log(3) + log(531441/524288) ≦ 21/e + 7153/(2^19)
log(3/2) ≦ (21/19e) + 7153/(19*2^19) = 0.40732166
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