Linux Log permissions
Solution 1:
Put those other users in their own group, make sure the logfiles belong to that group and make them group-readable.
Solution 2:
Basically what Manni said, but if you are using log rotate, when new logs are created you will want them to have those permissions too, so look at the create directive of logrotate.
There also might be a group in place for this on your distribution, such as the adm group in Ubuntu.