To log Mysql console session use option –tee (two dashes!) with full path to the log file:
mysql -uroot my_db --tee=/tmp/mysql_console.log
As result the file /tmp/mysql_console.log will contains all commands and queries with result of their executions. That might be helpful to keep your queries for using next time or for troubleshooting.
The author of the post, where I found that useful info, said that each time the Mysql session is started with logging the log file will be replaced. In my case it isn’t. As I expected the new messages just are appended to the log file.