Minecraft wiki entry for Development_versions, associated text: Now done using Log4j 2.
Default logging location is now in logs/latest.log, older logs are archived in logs/year-months-day-counter.log.gz with GZIP compress. The year is 4 digits, and the month and day are both 2 digits. The counter is the number of startups on the day. The counter is 1 when the first startup of the day and increasing each startup.
The way logs are saved can be changed, examples: HTML page, database, errors only, no logging at all.