I am such a fucking geek

Ok, so I'm up playing Star Wars: Knights of the Old Republic and I get to a point in the game where there's a mathematical challenge in order to do something in the game. Now they actually give you a few ways to get around this point, so you don't HAVE to do the mathematical part, but I decided to try it anyway.

Now the Challenge is rather simple, there's a sequence of numbers and you have to get the next number in the sequence from a selection of numbers.
Pretty easy, right?

Here they are:

Additive: 1, 2, 4, 7, 11, 16 (19, 22, 24, 31)
Subtractive: 21, 18, 16, 15, 15, 16 (14, 18, 19, 21)
Multiplicative: 1, 2, 4, 8, 16, 32 (48, 52, 64, 96)
Divisive: 128, 64, 32, 16, 8, 4 (2, 1, 0, -2)
Exponential: 1, 32, 81, 64, 25 (1, 3, 6, 9)
Logarithmic: 1 0 - 8 3 - 32 5 - 128 (5, 6, 7, 8)

Now the first 4 are pretty simple, but the 5th one stumped me. I went to look it up and even found the answer, but this is where the geekyness of me took over. I KEPT on searching for more and more answers to find out WHY it was the answer. In the end none of the walkthroughs, guides and FAQ's gave a reason as to why the answer was what it was, but I managed to figure it out in the end.

What's more of a tragedy, the fact that I'm up at 4 in the morning doing my laundry, the fact that I'm playing KOTOR at 4 in the morning, or the fact that I ended up trying to solve mathematical puzzles and got quite excited when I solved a more taxing one....?