I'm running MySQL on QSB... I don't use ltib to create my filesystem but debootstrap. The filesystem may be larger, but is a complete basic debian system.
Doing so gives me the opportunity to use the packet manager apt-get to install mysql.
apt-get install mysql-server
apt-get install mysql-client
If you do not have memory space restrictions I would generally suggest to use debootstrap giving you more flexibility.
You mentioned, that you don't get an output. Have you tried to enter "mysql" in your shell? Still getting no output?
Regards,
Rooney