Ideally, logo images for print are not jpg, because jpgs are not good
at clear detail (they use a compression system that actually reduces
detail each time they are saved).
A vector format that will take advantage of the precision of the
printing device is the best choice for a logo. Programs like Adobe
Illustrator or the open-source Inkscape are best suited to create
these types of images. Of course, recreating the image will involve
some work and require skill within the program; do you have access to
the original image before it was a jpg?