f（loga X）=（a/a^2-1)(x-1/x)
设logax=t,x=a^t
∴f(t)=a/(a²-1)*(a^t-1/a^t)
a>1时,
∵a^t递增,-1/a^t递增,a/(a²-1)>0
∴f(t)=a/(a²-1)*(a^t-1/a^t)为增函数
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