已知a>2.求证loga/log(a-1)>log(a+1)/loga

Question

已知a>2.求证loga/log(a-1)>log(a+1)/loga

Answer 1

首先用换底公式：
log(a-1)a=lga/lg(a-1)
loga(a+1)=lg(a+1)/lga
log(a-1)a/loga(a+1)=(lga)^2/lg(a-1)*lg(a+1)[1]
由均值不等式,
lg(a-1)*lg(a+1)