The APS sync log file can be found at the following location:
​%localappdata%\Business Fitness\Active Sync Desktop\logs\Sync.log

This is on the machine where the APS sync application is installed.
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If the APS sync is running but no errors are being logged in the above-mentioned log file, note that the file has an upper size limit of 1 GB. You may need to move the existing log file to a different folder. On the next sync run, the APS sync utility will automatically create a new log file in the same location and continue logging as usual.