if 4^x-4^(x-1)=24, What is the value of (2x)^x

I think that x=2.5 I used my calculator and not quite sure. I also am not quite sure how to do this by hand because on my test I cannot use the calculator. I can figure out by starting at zero and going up bu 1 its .75, 3, 12, 48 so so 24 is 2 times 12 so it is half between 2 and 3 thus 2.5. There has to be an easier way. Please help me