This is interesting question with at least couple options. So, let's dig in…
On 17th of January 2022, Michael Paquier committed patch:
Introduce log_destination=jsonlog "jsonlog" is a new value that can be added to log_destination to provide logs in the JSON format, with its output written to a file, making it the third type of destination of this kind, after "stderr" and "csvlog". The format is convenient to feed logs to other applications. There is also a plugin external to core that provided this feature using the hook in elog.c, but this had to overwrite the output of "stderr" to work, so being able to do both at the same time was not possible. The files generated by this log format are suffixed with ".json", and use the same rotation policies as the other two formats depending on the backend configuration. This takes advantage of the refactoring work done previously in ac7c807, bed6ed3, 8b76f89 and 2d77d83 for the backend parts, and 72b76f7 for the TAP tests, making the addition of any new file-based format rather straight-forward. The documentation is updated to list all the keys and the values that can exist in this new format. pg_current_logfile() also required a refresh for the new option. Author: Sehrope Sarkuni, Michael Paquier Reviewed-by: Nathan Bossart, Justin Pryzby Discussion: https://postgr.es/m/CAH7T-aqswBM6JWe4pDehi1uOiufqe06DJWaU5=X7dDLyqUExHg@mail.gmail.com
Just so that it will be perfectly clear: the logs I have in mind are the ones for DBAs to read – with slow queries, errors, and other interesting information.
So, how does one find them?
On 6th of April 2020, Amit Kapila committed patch:
Allow autovacuum to log WAL usage statistics. This commit allows autovacuum to log WAL usage statistics added by commit df3b181499. Author: Julien Rouhaud Reviewed-by: Dilip Kumar and Amit Kapila Discussion: https://postgr.es/m/CAB-hujrP8ZfUkvL5OYETipQwA=e3n7oqHFU=4ZLxWS_Cza3kQQ@mail.gmail.com
On 3rd of April 2019, Alvaro Herrera committed patch:
Log all statements from a sample of transactions This is useful to obtain a view of the different transaction types in an application, regardless of the durations of the statements each runs. Author: Adrien Nayrat