I have ventless gas logs in my fireplace. My fireplace is capped off right above them. When I'm using them, you can smell an odor that gets stronger the longer you have them on. It smells like gas fumes. I would like to fix this problem if it can be done. Any advice to alleviate this problem would be more than appreciated.

You could have a very dangerous situation. I suggest you obtain the services of a company with a CO tester to see how high the levels are in your home from operating them. You might also see if they can clean/adjust your logs so they burn cleaner. If those are a older log set they probably do not have a oxygen depletion safety sensor and if so I would never use them but replace them with a set that meets the current standards for safety.