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以3为底0.3的对数和以0.3为底3的对数，怎么比较大小

2025-03-16 04:52:00

推荐回答（2个）

回答1：

log3[0.3]=lg0.3/lg3=(lg3-1)/lg3=1-1/lg3

log0.3[3]=lg3/lg0.3=lg3/(lg3-1)=(lg3-1+1)/(lg3-1)=1+1/(lg3-1)=1-1/(1-lg3)

∵9＜10
∴lg9＜lg10
∴2lg3＜1
∴0＜lg3＜1-lg3
∴0＜1/(1-lg3)＜1/lg3
∴-1/lg3＜-1/(1-lg3)＜0
∴1-1/lg3＜1-1/(1-lg3)
∴log3[0.3]＜log0.3[3]

回答2：

-1=log(3)(1/3)=log(0.3)(1/0.3)1/3>0.3,1/0.3>3.因为log（3）（x）是增函数,log（0.3）（x）是减函数log(3)(0.3)

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