-- Synchrony database is not starting
-- binlog.0000xxx files from  ..\Synchrony_Database\binaries\data are missing or corrupt
-- ..\Synchrony_Database\binaries\data\*.err log shows:
"[ERROR] Failed to open log (file './binlog.000009', errno 2)",
or
[ERROR] I/O error reading the header from the binary log
and then "[ERROR] Could not open log file"   "Can't init tc log"  "Aborting"

The Synchrony database reads  ..\Synchrony_Database\binaries\data\binlog.index at startup and must find all binlogs referenced.

If the referenced binlog files can not be restored from backup the database can still be started by editing the binlog.index file to remove references to all missing binlog files.

IMPORTANT, any data that may have been recoverable from the missing binlogs will be lost. It will not be able to commit or roll back any changes that were pending at the time the database was last stopped.  Potentially not very serious if the database was stopped cleanly.
If this is a production system  and you are re-starting after an improper database shutdown or other crash, we recommend you consider restoring to a valid last known backup point; or monitor your system closely in case a re-install is needed due to database corruption.