The first question.

Because a is between 0 and 1, the function monotonically decreases in the interval. The maximum value is f(3) and the minimum value is f(5).

Loga(3)-loga(5)= 1。

That is loga(3/5)= 1.

So a=3/5.

The second question.

Find the monotone decreasing interval of function f(x), that is, find the monotone decreasing interval of function g(x)=|x- 1|.

Namely: (-∞, 1)

The third question.

(1) If a=-2

Then f (x) = LG (x 2-2x+8)

Because x2-2x+8 = x2-2x+1+7 = (x-1) 2+7.

Therefore, the range of easily obtained functions is [lg7, +∞).

(2) From the properties of composite functions, we can see that

F(x) monotonically increases on [2, +∞), that is, G (x) = x 2+ax-4a monotonically increases on [2, +∞).

That is, g'(x) is greater than or equal to zero in [2, +∞).

That is 2x+a >; =0 holds for x∈[2, +∞).

Easy to get a & gt=-4

So the range of a is [-4, +∞).