Be sure and get the right architecture for rsylogd modules.

I've tested this locally on 64-bit with:

dracut -a syslog -f -v foo.img `uname -r`

And I see this in the output:

I: *** Sourcing module syslog
I: Installing /sbin/rsyslogd
I: Installing /lib64/rsyslog/lmnet.so
I: Installing /lib64/rsyslog/imklog.so
I: Installing /lib64/rsyslog/imuxsock.so
I: Installing /usr/share/dracut/modules.d/98syslog/parse-syslog-opts.sh
I: Installing /usr/share/dracut/modules.d/98syslog/syslog-genrules.sh
I: Installing /usr/share/dracut/modules.d/98syslog/syslog-cleanup.sh
I: Installing /usr/share/dracut/modules.d/98syslog/rsyslogd-start.sh
I: Installing /usr/share/dracut/modules.d/98syslog/rsyslogd-stop.sh
I: Installing /usr/share/dracut/modules.d/98syslog/rsyslog.conf

modules.d/98syslog/install

@@ -3,7 +3,12 @@
 # ex: ts=8 sw=4 sts=4 et filetype=sh
 
 if type -P rsyslogd >/dev/null; then
-    installs="rsyslogd /lib/rsyslog/lmnet.so /lib/rsyslog/imklog.so /lib/rsyslog/imuxsock.so"
+    installs="rsyslogd"
+    for i in {"$libdir","$usrlibdir"}/rsyslog/lmnet.so \
+            {"$libdir","$usrlibdir"}/rsyslog/imklog.so \
+            {"$libdir","$usrlibdir"}/rsyslog/imuxsock.so ; do
+        [ -e "$i" ] && installs="$installs $i"
+    done
 elif type -P syslogd >/dev/null; then
     installs="syslogd"
 elif type -P syslog-ng >/dev/null; then