Have you tried making a really large Apple Logo in a Word Pro document.
Eg. Open Word or something similar, set it to a landscape format, choose a font that came with the system, choose a large font size, and press option-shift-K, then print it as a PDF, and then export as whatever file format you want so you can alter it. (Exporting the PDF as a JPG, and then in GraphicConverter, Inverse the colors gives the white on black logo.)
You can make an Apple logo any size you like. Open Adobe Illustrator and type Option-Shift-K. Select and choose Create Outlines from the Type menu. Scale to the size you want. This is a vector graphic, so it will display and print without distortion or "jaggies."