1、如果M=5×5×5×.×5(共2007个5相乘),N=2×2×2×.×2(1、如果M=5×5×5×......×5(共2007个5相乘),N=2×2×2×......×2(共4685个2相乘),请比较M和N的大小。
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![1、如果M=5×5×5×.×5(共2007个5相乘),N=2×2×2×.×2(1、如果M=5×5×5×......×5(共2007个5相乘),N=2×2×2×......×2(共4685个2相乘),请比较M和N的大小。](/uploads/image/z/1599197-5-7.jpg?t=1%E3%80%81%E5%A6%82%E6%9E%9CM%3D5%C3%975%C3%975%C3%97.%C3%975%28%E5%85%B12007%E4%B8%AA5%E7%9B%B8%E4%B9%98%29%2CN%3D2%C3%972%C3%972%C3%97.%C3%972%281%E3%80%81%E5%A6%82%E6%9E%9CM%3D5%C3%975%C3%975%C3%97......%C3%975%EF%BC%88%E5%85%B12007%E4%B8%AA5%E7%9B%B8%E4%B9%98%EF%BC%89%EF%BC%8CN%3D2%C3%972%C3%972%C3%97......%C3%972%EF%BC%88%E5%85%B14685%E4%B8%AA2%E7%9B%B8%E4%B9%98%EF%BC%89%EF%BC%8C%E8%AF%B7%E6%AF%94%E8%BE%83M%E5%92%8CN%E7%9A%84%E5%A4%A7%E5%B0%8F%E3%80%82)
1、如果M=5×5×5×.×5(共2007个5相乘),N=2×2×2×.×2(1、如果M=5×5×5×......×5(共2007个5相乘),N=2×2×2×......×2(共4685个2相乘),请比较M和N的大小。
1、如果M=5×5×5×.×5(共2007个5相乘),N=2×2×2×.×2(
1、如果M=5×5×5×......×5(共2007个5相乘),N=2×2×2×......×2(共4685个2相乘),请比较M和N的大小。
1、如果M=5×5×5×.×5(共2007个5相乘),N=2×2×2×.×2(1、如果M=5×5×5×......×5(共2007个5相乘),N=2×2×2×......×2(共4685个2相乘),请比较M和N的大小。
5^3=125
2^7=128
2007=669*3
4685=669*7+2
M=5×5×5×.×5(共2007个5相乘)
=5^2007
=5^(3*669)
=(5^3)^669
=125^669
N=2×2×2×.×2(共4685个2相乘)
=2^4685
=2^(7*669+2)
=(2^7)^669*2^2
=128^669*2^2
∵ 125^669<128^669*2^2
∴ M=5×5×5×.×5(共2007个5相乘)<N=2×2×2×.×2(共4685个2相乘)
我记得应该取对数来比较,㏒m=2007㏒5=2007+2007㏒2.5 ㏒n=4685
应该是这么计算,㏒2.5的值大概是多少,应该能查到吧
M=(5×5×5)×(5×5×5)......×(5×5×5) (共669对(5×5×5),也就是2007个5相乘)
N=(2×2×2×2×2×2×2)×......×(2×2×2×2×2×2×2)×2×2 (共669对(7个2相乘),并且多出两个2)
因为 (5×5×5)=125 < (2×2×2×2×2×2×2)=128
所以 N...
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M=(5×5×5)×(5×5×5)......×(5×5×5) (共669对(5×5×5),也就是2007个5相乘)
N=(2×2×2×2×2×2×2)×......×(2×2×2×2×2×2×2)×2×2 (共669对(7个2相乘),并且多出两个2)
因为 (5×5×5)=125 < (2×2×2×2×2×2×2)=128
所以 N的669对的7个2连乘 比 M的669对的3个5连乘 大
而且N还多出了2个2
答案 M
收起
M>n
答案 M
2^7=128
2007=669*3
4685=669*7+2
M=5×5×5×......×5(共2007个5相乘)
=5^2007
=5^(3*669)
=(5^3)^669
=125^669
N=2×2×2×......×2(共4685个2相乘)
=2^4685
=2^(7*669+2)
=(2^7)^669*2^2
=128^669*2^2
∵ 125^669<128^669*2^2