That depends on whether you want visible stitches or not. You can sew anything fabric to anything fabric, and sewing a logo onto spandex is easy-peasy - but it does leave clear stitches whether you edge-stitch (a needle's-width in from the edge) or satin-stitch (use a tight zig-zag like you see on patches). If you don't, then use FABRIC GLUE. You do still need to stretch the spandex so like harmfulAdam said, wear it while someone else applies it or stretch it on a dress form, but I strongly recommend fabric glue, like Fabri-Tac or even Gem-Tac (which holds rhinestones onto fabric, works where nothing else will). It should be tacky and when dry, it will hold solid even on a stretch fabric. After all, that's how gymnasts' costume designers hold all the rhinestones to their leotards.
Alternately, you can use Heat N Bond to iron the logo on, but I have had a lot of trouble lately getting Heat n Bond to permanently stick like it's supposed to - I usually use it to tack down appliques before I sew them for a stronger hold than pins. Technically, Heat n Bond is supposed to be the ultimate in no-sew methods to apply fabric to fabric but like I say...it doesn't really hold permanently.
