The logging.json file is usually located in the specified --config-dir, the same directory as the config.ini file. This path can be explicitly defined using the -l or --logconf options when starting nodeos.
nodeos --help...
Application Command Line Options:
...
--config-dir arg Directory containing configuration files such as config.ini
-l [ --logconf ] arg (=logging.json) Logging configuration file name/path for library users