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If you send the same imge to the printer and specify a physical dimension such as 5 inches by 5 inches using 300dpi the image would have to be scaled up because there isn't enough pixels. This will produce a soft and blurry image.
Confused yet? :P scale your image before sending it to the printer.
If you have the time and the inclination, learn to make logo's using a vector application. It will never need scaling, will be true at any resolution and is portable and editable for all formats.
You could even use the selection to create a work path so you don't have to redraw it.
Illustrator is the best tool, a little steep to learn at first, but as soon as you have nodes and pen tool sussed you'll wonder why you ever used Photoshop for this.