You create the logo in a desktop application for which you need the desktop font – thus you have to purchase the desktop license.
As the font software will be converted to an image in the logo (e.g. gif/jpg/png) and you distribute the image of the font, not the font software itself, no additional licensing is required.
For further details, please read the End User License Agreement of the font you want to use for your logo.
Please note not all foundries allow the creation/distribution of a logo with the desktop license but require a special license for this usage.