time machine excludes some files and directories by default, the list can be found in
/System/Library/CoreServices/backupd.bundle/Contents/Resources/StdExclusions.plist
a description of the plist in Time Machine Exclusions shows that some log files/paths were excluded in 10.5, and even more excluded in 10.6 (see Designed to Fail: ...). the motivation to exclude /private/var/log directory is pretty clear, it is changing rapidly especially because of log rotation. actually, Apple does not use backup-friendly scheme for log rotation:

$ ls -alt /var/log/system.log*
-rw-r----- 1 root admin 59536 Apr 17 00:54 /var/log/system.log
-rw-r----- 1 root admin 24823 Apr 17 00:30 /var/log/system.log.0.bz2
-rw-r----- 1 root admin 13872 Apr 16 00:30 /var/log/system.log.1.bz2
-rw-r----- 1 root admin 13690 Apr 15 00:30 /var/log/system.log.2.bz2
-rw-r----- 1 root admin 18642 Apr 14 00:30 /var/log/system.log.3.bz2

log system.log is compressed every night at 00:30 and all the compressed files are renamed so that the most recent archive is system.log.0.bz2, the files in backup should be updated. the better scheme is to use date instead of numbers for numbering the compressed files.

time machine and renamed files

briefly: time machine does not recognize renamed files and folders. if you simply rename a folder containing 1Gb of files without touching data inside, you'll waist extra 1Gb of backup space. more on this issue in Time Machine: Some Details

named backups in time machine

it's a pity that apple time machine does not allow to give a name or a note for a backup. unfortunately it is not possible push the button "back up now" and give a reason for this manual backup. it would be really useful for search, when you do not know thew date. additionally it would be good to keep such backup longer (forever?).