The Maltego client's log file can be found in the following directories depending on which operating system you are using:

Windows:

C:\Users\<username>\AppData\Roaming\.maltego\v<maltego_version>\var\log\

OS X:

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

Linux:

~/.maltego/v<maltego_version>/var/log/

OR

Go to Application Menu > Tools > Open Logs Folder.