First, 4c-a & gt；; = b & gt=0，c/a & gt； = 1/4 ; 5c-3a & lt； =4c-a，c/a & lt； =2

Make b/a < =2*4- 1=7, especially when b/a=7, the second inequality holds. The equal sign is true if and only if a:b:c = 1:7:2.

And c ln b≥a+c ln c knows 0.

Therefore, b/a >; =(b/c)/ln(b/c), let the function f (x) = x/ln (x). (x >； 1) from the derivative knowledge, we know that the minimum value of the function is e, so b/a >; =e，

The equal sign is true if and only if b/c = e and b/a = e. Substitute into the first inequality: 2

Therefore, the value range of b/a is [e, 7 double closed interval.

Of course, this problem may be solved from the perspective of geometry, that is, the knowledge of linear programming. This question mainly examines the range of inequality variables, mainly examines whether the = sign is established and needs to be verified separately. This question is a bit difficult. Personally, I don't think the college entrance examination should examine the range of values, because in a broad sense, filling (0,+infinity) should be correct! The title itself is a bit ambiguous. Of course, the value range of this question is essentially the value range of 2 yuan function, but you can't directly say the value range on the college entrance examination paper, because it is suspected of exceeding the outline, and using the value range can make candidates show their talents. Unfortunately, it's just a fill-in-the-blank question. There are some innovative elements in this problem. I think it is mainly aimed at students from Peking University and Tsinghua! Bless the students in Jiangsu!