If you have to privileges you should be able to see it. You may have to change your Thread Layout from Minimalist to Vertical or another built in layout.
So to expand on what Nullified stated. I can only see this from my Admin account. On the left hand side of the post in the information box right below the name and rank it will show the IP of the person that posted. This is the only way I know how to find it for an application.
-- Six Demon Bag Jack Burton: Hey, what more can a guy ask for? Egg Shen: Oh, a six-demon bag! Jack Burton: Terrific, a six-demon bag. Sensational. What's in it, Egg? Egg Shen: Wind, fire, all that kind of thing!
All answers are correct. Just look under the name "Application" on the left. For non-admins, it'll show "Poster's IP: Logged", but for you, if you're logged in as admin, it should should "Poster's IP: XXX.YYY.ZZZ.AAA"