Check out the security tips page.
http://httpd.apache.org/docs/2.2/misc/security_tips.html
If you allow non-root users to modify any files that root either
executes or writes on then you open your system to root compromises.
For example, someone could replace the httpd binary so that the next
time you start it, it will execute some arbitrary code. If the logs
directory is writeable (by a non-root user), someone could replace a
log file with a symlink to some other system file, and then root might
overwrite that file with arbitrary data. If the log files themselves
are writeable (by a non-root user), then someone may be able to
overwrite the log itself with bogus data.
Since apache opens and reads the log file as root, there is a danger here for abuse. Not sure why you would want a non-root (apache) user to have write access to the files. You can safely grant read access but would suggest that write access only be given to old files that have rotated. Apache is not opening these files when you use logrotate to manage log rotation.
gain access to the uid that the server is started as
they gave you the answer already.