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)