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阿Q吧 > lg4 * lg4 ⼀ (lg3 * lg5) >1怎么证明

lg4 * lg4 ⼀ (lg3 * lg5) >1怎么证明

2025-03-15 01:35:55

推荐回答（4个）

回答1：

由对数函数单调递增可知 2lg4 >lg3+lg5 >0
对前个不等号两边平方可得
4lg4 * lg4 >(lg3 )^2+ (lg5)^2+2lg3lg5
运用基本不等式(lg3 )^2+ (lg5)^2>2lg3lg5
所以4(lg4 )^2>4lg3lg5
即原不等式成立

回答2：

lg4 * lg4 =lg16
lg3 * lg5=lg15
因为16>15，所以lg16>lg15
所以命题成立

回答3：

lg4 * lg4 / (lg3 * lg5) 等价 4 * 4 /3 *5= 16/15>1

回答4：

EXCEL计算
lg4 * lg4 / (lg3 * lg5)=1.086906619>1
完毕

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