If you are talking about the transparency effects in InDesign and Illustrator, the .eps format doesn't support transparencies. You don't need to get the file into Illustrator to save it as a .eps. ac6789 was right, just export it as a .eps.
It will flatten or rasterize any transparencies you may have, though.
If you have any of those special effects in your file, and you need to get it into Illustrator, the best way I've found is to save it as a later version .pdf. The newer versions of .pdf support transparencies and don't flatten them. Then just open the .pdf in Illustrator and go from there.
Is there any reason that you didn't create your logo in Illustrator? Illy has more tools for art creation and manipulation than InDesign does. InDesign isn't really made for that kind of work, it's more a page layout program, like Quark.
If you have a raster image included as part of the logo (the only reason I can think of using live trace), you can bring that type of art into Illustrator as well, and bypass InDesign altogether. Just open a new file in Illustrator, and go to Edit, Place Image, and navigate to where your image is located.
I just wish Adobe would put into Illustrator the ability to open InDesign files, natively. I think it's stupid to have to jump through hoops to get art from ID to Illustrator, I hate that.