If the function f (x) = loga [1 - (2a-1) x] is an increasing function in the interval [2,4], then the value range of a I know the answer. But why can't I get the interval

If the function f (x) = loga [1 - (2a-1) x] is an increasing function in the interval [2,4], then the value range of a I know the answer. But why can't I get the interval

x=2 1-2(2a-1)>0 a0 a