SQL Server will not cycle errorlogs unless you restart the instance. This behavior dates from the very early days (SQL Server 6.5 or even older) when not much stuff was written to the log.
If you need to cycle the logs manually because the current log has gotten too big, you can call the system procedure sp_cycle_errorlog. If you would like to cycle the log on a regular basis, you can schedule a job to do this once a day/week/month if you like.
All of that said, so many entries in the server log in only a few days time seems excessive. You might want to look at those entries and investigate any entry that occurs often. If you are getting lots of login/logout messages, for example, you might reconsider your auditing policy.