I am making DIY logo for myself small business.
Are open source fonts safe to use anything?
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Everything depends on the license of the font in question. For instance - if the font is published under OFL (SIL Open Font License) - you can use it for commercial proposes as well (use it as a font, not to sell it...) The best resource on internet for free for commercial use fonts is [Fontsquirrel] (https://www.fontsquirrel.com/) - the fonts are organized by categories, and there is all the information about the licence and use permissions for each typeface.
Fonts, like other media, have varied licenses. Some can be used and distributed freely, but others must be licensed. Microsoft has a help page on this very subject.
Most of the fonts supplied with Microsoft products have been licensed from leading type foundries. In most cases Microsoft does not have the right to sublicense them. You can use Microsoft's free Font properties extension to find out who to contact regarding licensing issues.
The same applies to the fonts provided with other operating systems. It's best to do some research before using them (either to find open alternatives or purchase the appropriate licenses).
You said your business is small, so it might be best to use fonts with permissive licenses. Many great tools are available to help with this, but a good place to start is Google Fonts, which provides hundreds of open-source typefaces.
Best of luck!