In Maltego 4.1 and later

Maltego 4.1 and later includes an option to open your client logs folder from the application menu.

Click the application icon in the top left corner, hover over "Tools" and click "Open Logs Folder"

Opening the logs folder manually

By default, the client log files should be stored in the following directories:

On Windows:

On Linux:

On Mac:
/Users/< user >/Library/Application Support/maltego/v<maltego_version>/var/log