log(2)(a)=log(3)(b)=log(5)(c)
问题描述:
log(2)(a)=log(3)(b)=log(5)(c)
数学人气:960 ℃时间:2020-02-03 15:17:21
优质解答
设:x=log(2)(a)=log(3)(b)=log(5)(c)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所以:c^(1/5)>a^0.5>b^(1/3)
因为:5^6=25^3所以:c^(1/5)>a^0.5>b^(1/3)
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答
设:x=log(2)(a)=log(3)(b)=log(5)(c)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所以:c^(1/5)>a^0.5>b^(1/3)