Is LOG4 Net is cross platform ?
For details on Log4Net you'll have to ask the Log4Net folks. Looking at their supported frameworks page (https://logging.apache.org/log4net/release/framework-support.html ) it supports .Net Standard, and so should run in all .Net 6 platforms.
You can also find the same information on the compatibility matrix on the package's Framework page on nuget: https://www.nuget.org/packages/log4net/
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