If CiviCRM has logging enabled, then an extension is installed that creates its own tables, CiviCRM attempts to log writes to those tables and fails when they do not exist. See https://github.com/JMAConsulting/biz.jmaconsulting.mte/issues/48.
I think solution is:
a) don't log to these tables, or
b) extend logging support to extension system.
Alternatively, add documentation to admin page where logging gets enabled about this Known Issue indicating how to manually create the needed log tables for extensions.