数学问题：已知a>2,求证Loga(a-1)×Loga(a+1)<1

由a>2得

loga(a+1)>0,loga(a-1)>0

所以：

loga(a+1)*loga(a-1)

<[loga(a+1)+loga(a-1)]^2/4 （均值不等式）

=[loga(a^2-1)]^2/4

<[loga(a^2)]^2/4

=2^2/4

=1