If you are using the direct-download version of Decibel the log is saved to ~/Library/Logs/Decibel.log.
If you are using the app store version of Decibel the log is saved to ~/Library/Containers/org.sbooth.Decibel/Data/Library/Logs/Decibel.log.
The log is overwritten at each launch of Decibel.
The easiest way to locate the log file is to use the Go To Folder... command in Finder's Go menu:
And then enter the appropriate location for your version:
