The Fade In application log file, generated while it is running, can be found at:

Windows:
C:\Users\AppData\Roaming\Fade In (Vista/Windows 7 and later); or
C:\Documents and Settings\Application Data\Fade In (XP and earlier)

Mac OS X:
/Users/Library/Application Support/Fade In; or
/Users/Library/Containers/com.generalcoffee.fadein/Data/Library/Application Support/Fade In (Mac App Store version)

Linux:
~/.local/share/fadein
(Note: For older versions of Fade In, this directory was: ~/.fadein.)