a＞2,求证loga（a-1)乘loga（a+1）＜1

题目

a＞2,求证loga（a-1)乘loga（a+1）＜1

答案

证明:
∵a>2
∴a-1>1
∴loga(a-1)*loga(a+1)>0
∴2√[loga(a-1)*loga(a+1)]
≤ loga(a-1) +loga(a+1)
= loga(a^2 -1)
< loga(a^2) = 2
∴loga(a-1)*loga(a+1)<1
证毕