As log files can easily get lost, the best way to approach making sure autovacuum is doing what it should is to monitor what tables it's worked on instead:
SELECT schemaname,relname,last_autovacuum,last_autoanalyze FROM pg_stat_all_tables;
You can trim down the information here by changing all in the preceding code to name one of the alternate views: pg_stat_sys_tables shows only system tables, while pg_stat_user_tables shows only your user tables.