Question

■■■■【高一数学 对数】■■■■

=>lg(n/(n-1))>lg((n+1)/n)>0
=>lgn/lg(n-1)>lg(n+1)/lgn>0
lg(n/(n-1))不是等于lgn-lg(n-1)
为什么可以直接这样写呢？

Answer 1

n>2
lgn>lg(n-1)>0
=>1+1/(n-1)>1+1/n>1
=>n/(n-1)>(n+1)/n>1
=>lg(n/(n-1))>lg((n+1)/n)>0
=>lgn/lg(n-1)>lg(n+1)/lgn>0
=>(lgn)^2>lg(n+1)lg(n-1)