No, they are always going to be in the FMS folder. You could uninstall FMS and reinstall it on another drive...
open comand prompt as administrator
cd C:\Program Files\FileMaker\FileMaker Server\
ren Logs Logs.old
mklink /D Logs anyotherfoldertouse
I saw the logs are created in anyotherfoldertouse (in another drive),
but i don't know this is safe or not.