The Maltego Desktop Client's log file can be found in the following directories depending on which operating system you are using:
Windows:
Maltego 4.3.X and above:
C:\Users\<username>\AppData\Roaming\maltego\v<maltego_version>\var\log\
Maltego 4.2.19 and below:
C:\Users\<username>\AppData\Roaming\.maltego\v<maltego_version>\var\log\
Note: Please ensure that you replace <username> with your username, and v<maltego_version> with your current Maltego version, e.g. v4.2.19.
OS X:
/Users/<username>/Library/Application Support/maltego/v<maltego_version>/var/log
Note: Please ensure that you replace <username> with your username, and v<maltego_version> with your current Maltego version, e.g. v4.2.19.
Linux:
~/.maltego/v<maltego_version>/var/log/
Within the Maltego Desktop Client
Alternatively, you can go to Application Menu > Tools > Open Logs Folder.