Then the discriminant of x 2-2ax+3 = 4a 2- 12.

2,f(x)=log4(ax^2+2x+3)。

①f( 1)= log4(a+2+3)= 1、a+5=4、a=- 1 .

② If the minimum value of f (x) = log4 (ax 2+2x+3) is 0, the minimum value of y = ax 2+2x+3 is 1.

A>0 and a (-1/a) 2+2 (-1/a)+3 =1,a= 1/2.

3，f(x)=loga(x).

| loga(x)| & gt； 1, namely loga (x)

When 0

Because x & gt=3, x> 1/a, a>1/x.

The maximum value of 1/x is 1/3, so 1/3.

When a> is 1, 0

Because of x>3, x> answers.

The minimum value of x is 3, so 1

In a word, the range of a is (1/3, 1)U( 1, 3).