Ivanjam's solution is pretty much spot on. However, I have one other suggestion to add.
On a problem like this, if you can't figure it out analytically, try to use an actual number. So let's say your list has n=64 items in it. (We pick 64 because we see all those log_2's in our answer, and it's nice to take the log_2 of a power of 2.)
Now, suppose that you have the worst case scenario - that you keep going until you have a list of 1. So let's take a look at how many steps it takes.
64 items gets cut down to 32. Then 32 -> 16, 16 -> 8, 8 -> 4, 4 ->2, and finally 2 -> 1 and we're done. So it seems that it took 6 steps to get from 64 down to 1.
Let's look at our answers now:
(D) 64 * 6
(E) 64² * 6
Our only possible candidate therefore is (C).