log(2)(a)=log(3)(b)=log(5)(c)
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log(2)(a)=log(3)(b)=log(5)(c)
log(2)(a)=log(3)(b)=log(5)(c)<0,求a^0.5,b^(1/3),c^(1/5)这三个数的大小关系
log(2)(a)=log(3)(b)=log(5)(c)
设:x=log(2)(a)=log(3)(b)=log(5)(c)<0,则:a=2^x,b=3^x,c=5^x,
于是:a^0.5=(2^15)^(x/30),b^(1/3)=(3^10)^(x/30),c^(1/5)=(5^6)^(x/30),
因为:5^6=25^3<32^3=2^15=8^5<9^5=3^10,x/30<0
所以:c^(1/5)>a^0.5>b^(1/3)
a^0.5 < b^(1/3) < c^(1/5)
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