Using file .log.3.gz
mysql.log files is where some distros store the MySQL error log. It contains errors, warnings, notes and every time that MySQL has started and stopped.

mysql.log.3.gz is the third archived log, and if there is no mysql.log.4.gz, the latest before the currently being written now. So, it is probably not the latest (current) log.

If you had a UNIX console, the first thing I would do is:

zgrep ERROR mysql.log.3.gz | wc -l  # count how many errors are there

zgrep ERROR mysql.log.3.gz | tail   # show the latest errors


You will see that it contains timestamps, which will give you an idea of the time frame.

zgrep and zless (using the search function /) are good tools to search for specific patterns on compressed files. There are some equivalents on Windows.

Please note that depending what was happening at the time, you may find many useless errors (already corrected) or warnings that are more important than the errors ("table missing, ignoring it").