Open Console app and type backup in the filter at the top and you can scroll through log entries related to TM and they will show the date/time of the backups.
Image
thanks for your reply,
followed your command ...
>complete amateur < ... still donut know what I'm looking for ... this is what i found when entering the the search field ...
11/08/2014 22:29:10.270 com.apple.backupd[480]: Starting automatic backup
11/08/2014 22:29:10.474 com.apple.backupd[480]: Attempting to mount network destination URL: afp://;AUTH=No%20User%20Authent@Space._afpovertcp._tcp.local/TM
11/08/2014 22:29:12.884 com.apple.backupd[480]: Mounted network destination at mount point: /Volumes/TM using URL: afp://;AUTH=No%20User%20Authent@Space._afpovertcp._tcp.local/TM
11/08/2014 22:30:11.000 kernel[0]: hfs: mounted Time Machine Backups on device disk2s2
11/08/2014 22:30:13.109 com.apple.backupd[480]: Disk image /Volumes/TM/Stuart.sparsebundle mounted at: /Volumes/Time Machine Backups
11/08/2014 22:30:13.885 com.apple.backupd[480]: Backing up to /dev/disk2s2: /Volumes/Time Machine Backups/Backups.backupdb
11/08/2014 22:31:07.970 com.apple.backupd[480]: Will copy (1.43 GB) from Macintosh HD
11/08/2014 22:31:07.973 com.apple.backupd[480]: Found 1857 files (1.43 GB) needing backup
11/08/2014 22:31:08.613 com.apple.backupd[480]: 2.85 GB required (including padding), 539.1 GB available
11/08/2014 22:34:43.463 com.apple.backupd[480]: Copied 2095 items (1.43 GB) from volume Macintosh HD. Linked 2926.
11/08/2014 22:35:27.422 com.apple.backupd[480]: Will copy (1.5 MB) from Macintosh HD
11/08/2014 22:35:27.423 com.apple.backupd[480]: Found 21 files (1.5 MB) needing backup
11/08/2014 22:35:27.424 com.apple.backupd[480]: 1.14 GB required (including padding), 539.1 GB available
11/08/2014 22:35:36.980 com.apple.backupd[480]: Copied 25 items (1.5 MB) from volume Macintosh HD. Linked 253.
11/08/2014 22:35:52.447 com.apple.backupd[480]: Created new backup: 2014-08-11-223549
11/08/2014 22:36:05.089 com.apple.backupd[480]: Starting post-backup thinning
11/08/2014 22:36:05.307 com.apple.backupd[480]: Error: Error Domain=NSOSStatusErrorDomain Code=-50 "The operation couldnt be completed. (OSStatus error -50.)" (paramErr: error in user parameter list) deleting backup: /Volumes/Time Machine Backups/Backups.backupdb/Stuart/2014-08-11-223021.inProgress/6C72E046-D8A5-40B9-BB8B-C85E1A4AD9B7
11/08/2014 22:36:15.761 com.apple.backupd[480]: Deleted /Volumes/Time Machine Backups/Backups.backupdb/Stuart/2014-08-10-215533 (6 MB)
11/08/2014 22:36:15.761 com.apple.backupd[480]: Post-backup thinning complete: 1 expired backups removed
11/08/2014 22:36:17.988 com.apple.backupd[480]: Backup completed successfully.
11/08/2014 22:36:30.000 kernel[0]: hfs: unmount initiated on Time Machine Backups on device disk2s2
11/08/2014 22:36:34.099 com.apple.backupd[480]: Ejected Time Machine disk image: /Volumes/TM/Stuart.sparsebundle
11/08/2014 22:36:34.250 com.apple.backupd[480]: Ejected Time Machine network volume.
... but , mac hasn't been asleep when all the above has happened i don't think