Think of yourself as a carpenter and the client has hired you to trim out a house. You buy the tools, the client pays for the final product (the trim being installed). You walk away with the tools you bought as part of doing business.
This is the same with fonts. It's a tool that you as a graphic designer use to produce work for clients. Since the logo doesn't need to retain the font data (assuming you are converting it to outlines) there's no need for the client to have a license for that font.(*)
If the client needs to use the font for other purposes, then they'd need to get their own license of the font--in addition to yours.
(*) There are some exceptions in that some typefaces have special licenses that require an additional license if the typeface is being used as a logo for a rather large entity. This is rare, but read the EULA to be sure.