Analysis: draw the image of the function f(x), then display 0 < a < 1, b > 1, ab= 1 by combining numbers and shapes, and then turn the required a+2b into a univariate function about a, and use the monotonicity of the function to find the range of the function.

Solution: Solution: Draw an image of y=|lgx|, as shown in the figure:

∫0 < a < b and f(a)=f(b),

∴|lga|=|lgb| and 0 < a < 1, b > 1.

∴-lga=lgb

That is ab= 1.

∴y=a+2b=a+2a,a∈(0, 1)

∫y = a+2a is the decreasing function at (0, 1),

∴y> 1+2 1=3

The range of ∴a+2b is (3, +∞).

So the answer is? (3,+∞)