Solution: First draw the image of function f(x)=logax on the coordinate plane.

Then the image part below the X axis is "folded" to the upper part of the X axis,

The image of the function g(x)=|logax| consists of the part * * of f(x) that is not below the X axis.

∫g( 1)= 0，g(a)=g ( 1a)= 1，

According to the chart, if the range of the function g(x) is [0, 1],

Its domain may be [1a, 1], [1, a], [1a, a],

And1-1a = a-1a < a-1,

Therefore, combined with the meaning of the question, 1- 1a= 56,

a=6。