23/02/01 19:27:40.88 ZonduRya.net
>>309
(1)
11^2=121＜128=2*8^2 → 11＜8√2
45^2=2025＜2048=2^11＜2^8√2 → 45＜2^4√2
(2) a＞46ではなく、a＞48を示す
10^3=1000＜1024=2^10 → 3/10＜Log10(2)
2^13=8192＜10000=10^4 → Log10(2)＜4/13 → 3/10＜Log10(2)＜4/13
3^5=243＜256=2^8 → Log10(3)＜(8/5)Log10(2)＜(8/5)*(4/13)=32/65=0.4923...
Log10(2^(4√2)/48)=4(√2-1)*Log10(2)-Log10(3)＞4*(1.414-1)*0.3-0.4924=0.0044>0 → 2^(4√2)＞48
(3)
2^1000=1.0715...*10^301 → Log10(2)＞0.301
Log10(2^(4√2)/50)=(4√2)*Log10(2)+Log10(2)-2＞(4*1.414+1)*0.301-2=0.00345...>0 → 2^(4√2)＞50
ちなみに a＜51 は、17^2=289＞288=2*12^2 → 17＞12√2 �