自定义nginx配置变量未扩展

我正在运行Nginx版本1.2.8.

以下配置中的$log和$elog似乎没有扩展,因此没有记录任何内容.这是问题,我怎样才能让它们扩展？

Nginx配置：

server {
    listen              xx.xx.xx.xx:80 default;
    server_name         domain.com;
    set                 $docroot                /home/domain.com/public_html;
    set                 $log                    /home/domain.com/logs/access_log;
    set                 $elog                   /home/domain.com/logs/error_log;
    root                $docroot;
    error_log           $elog;
    include             /etc/Nginx/http-BACkend.conf;

}

/etc/Nginx/http-BACkend.conf配置：

.....
LOCATIOn ~* ^.+\.(jpg|jpeg|gif|png|svg|css|mp3|ogg|mpe?g|avi|zip|gz|bz2?|rar|ico|swf|txt|tgz|tbz|pdfpls|torrent)${
    root                $docroot;
    try_files           $uri @fallBACk;
    access_log          $log            main;
    error_log           $elog;
    expires             30d;
    add_header          Pragma          "public";
    add_header          Cache-Control   "public";
#    error_page         404 = @fallBACk;
}
.....

UPD：感谢Valery Viktorovsky我通过更改日志文件夹的权限来解决这个问题.

chown -R apache.root /home/*/logs/
chmod -R 750 /home/*/logs/

提到的解决方法略有修改,也已应用.没有它,即使拥有正确的权限,它也无法运行. $log和$elog的值保持不变,但是添加了斜杠.

更新了/etc/Nginx/http-BACkend.conf配置：

.....
LOCATIOn ~* ^.+\.(jpg|jpeg|gif|png|svg|css|mp3|ogg|mpe?g|avi|zip|gz|bz2?|rar|ico|swf|txt|tgz|tbz|pdfpls|torrent)${
    root                $docroot;
    try_files           $uri @fallBACk;
#    access_log          $log            main;
#    error_log           $elog;
    access_log          /$log            main;
    error_log           /$elog;
    expires             30d;
    add_header          Pragma          "public";
    add_header          Cache-Control   "public";
#    error_page         404 = @fallBACk;
}
.....

仍然存在问题,因为apache使用所有者root创建日志文件.
为了部分解决这个问题,在logrotate配置中添加了相同的命令：

/home/*/logs/*_log {
    missingok
    notifempty
    weekly
    minsize 50M
    compress
    rotate 60
    sharedscripts
    postrotate
        /sbin/service Nginx reload > /dev/null 2>/dev/null || true
        /sbin/service httpd reload > /dev/null 2>/dev/null || true
        chown -R apache.root /home/*/logs/ > /dev/null 2>/dev/null || true
        chmod -R 750 /home/*/logs/ > /dev/null 2>/dev/null || true
    endscript
}