To perform point-in-time-recovery on a server after restoring a backup image, you need to know where to begin restoring incremental backups from the binary log.

If you set up a replication slave by populating it with a backup image from the master, you need to know where to tell the slave to begin reading the master binary log.

Use the mysqlbackup program with the --summary option to examine the backup image and check the Binlog coordinates line in the output:

shell> mysqlbackup --summary image.bak
...
Binlog coordinates:  binlog.002795:196

The output indicates that the coordinates are log file binlog.002795, position 196.

On the host where the backup was performed, if you know the backup_id value for the the backup operation that created the image file, you can use it to check the corresponding row in the backup_history log. Suppose that the backup operation produced this result:

mysql> BACKUP DATABASE * TO '/tmp/data.bak';
+-----------+
| backup_id |
+-----------+
| 5513      |
+-----------+

The backup ID is 5513. Use that value to find the binary log coordinates for the backup operation:

mysql> SELECT binlog_file, binlog_start_pos
    -> FROM mysql.backup_history WHERE backup_id=5513;
+---------------+------------------+
| binlog_file   | binlog_start_pos |
+---------------+------------------+
| binlog.002795 |              196 |
+---------------+------------------+

This example assumes that backup_history_log is set to ON and that the value of log_backup_output includes the TABLE destination. If the value includes only FILE logging, you must search the backup history log file manually.