Is it vector artwork created in Illy?
A JPEG file is a last resort to just see what things (do not) look like.
As I said, I know very little. The logo (I had done by a designer) is made up of various components and text ... each piece can be altered separately. Does that help?
If you need to send the printer a .jpg file, use File > Export. In the Export dialog box, select color mode = CMYK; Resolution 300ppi; set the compression at maximum ( 12 ). If you: Print > Save As > PDF; I believe the PDF takes on the document's resolution setting. Check in your Print > Resolution ( I'm not in CS5, so I don't know where it is located, but look for document resolution / raster resolution settings ) and set the output resolution to 2540 dpi / 300 ppi respectfully. These settings will give you smooth vectors and bitmaps. I prefer to use Acrobat Pro's "Distiller" to create final PDF files. Distiller will give you more control over settings. Either way, a PDF is the preferred file format when sending to outside print vendors. It always pays to talk with the actual print vendor and get their preferred file format workflow specs. If you are not sure how to proceed, bring the .ai and support files to a local printer. They may help you create the PDF ( for a fee ) or have a step-by-step procedure you can follow.