DreamHost users do not have access to MySQL server logs. However, depending on which type of MySQL server your databases are running on, it may be possible for support to retrieve them for you.
Shared MySQL servers
Visit the MySQL Databases page. You'll see a list of all of your hostnames and databases. At the top of the section, your database name is listed. If it is a specific name, this means you're on a Shared MySQL server. For example:
Unfortunately, logs are not available on Shared MySQL servers. This means that even technical support would be unable to retrieve them for you.
Private MySQL servers
Visit the MySQL Databases page. You'll see a list of all of your hostnames and databases. At the top of the section, your database name is listed. If the name starts with psmysql and is followed by a number, this means you're using a private MySQL server. For example:
Logs on a private MySQL server are available only if you contact technical support. Make sure to specify the database name and time frame you wish to retrieve logs from.
Dedicated servers and DreamCompute
On a Dedicated server, the MySQL databases are on the same machine. This means you can retrieve them by logging into the server via SSH.
DreamCompute is completely configured manually, so any configuration is completely up to you.