Apache Solr Admin on Tomcat Deployed in WebApps Directory

I am trying to get Apache Solr to work on Redhat6 and Tomcat6 (using these instructions), but get this error when browsing to the admin section, http://localhost:8080/solr-example/admin:

HTTP Status 404 - missing core name in path

type Status report

message missing core name in path

description The requested resource (missing core name in path) is not available.

http://localhost:8080/solr-example loads fine, with a link to "Solr Admin."

My setup is as follows:

tomcat6: /etc/tomcat6
Solr: /app/solr/example

I have a solr-example.xml in /etc/tomcat6/Catalina/localhost/, which reads:

<?xml version="1.0" encoding="utf-8"?>
<Context docBase="/app/solr/example/apache-solr-3.4.0.war" debug="0" crossContext="true">
  <Environment name="solr/home" type="java.lang.String" value="/app/solr/example" override="true"/>
</Context>

I don't see anything in the logs (/var/log/tomcat6) ... only entires in catalina.out are regarding the starting and stopping of tomcat6.

My questions are:

1.What else do I need to do to get "Solr Admin" to work under Tomcat?

2.Where are these "cores" supposed to be specified? I see an entry in /app/solr/example/solr/solr.xml ?

<solr persistent="false">
      adminPath: RequestHandler path to manage cores.  
        If 'null' (or absent), cores will not be manageable via request handler
      <cores adminPath="/admin/cores" defaultCoreName="collection1">
        <core name="collection1" instanceDir="." />
      </cores>
    </solr>

3.How do I got about ensuring that logs are working correctly? I can't find logs that contain mention of the 404 above.

Update in response to @quanta's comment:

1. Downloaded former (apache-solr-3.4.0.tgz)
2. dataDir was not set, now set to: <dataDir>${solr.data.dir:../solr/data}</dataDir>
3. JAVA_OPTS: /usr/lib/jvm/java/bin/java -classpath :/usr/share/tomcat6/bin/bootstrap.jar:/usr/share/tomcat6/bin/tomcat-juli.jar:/usr/share/java/commons-daemon.jar -Dcatalina.base=/usr/share/tomcat6 -Dcatalina.home=/usr/share/tomcat6 -Djava.endorsed.dirs= -Djava.io.tmpdir=/var/cache/tomcat6/temp -Djava.util.logging.config.file=/usr/share/tomcat6/conf/logging.properties -Djava.util.logging.manager=org.apache.juli.ClassLoaderLogManager org.apache.catalina.startup.Bootstrap start
4. catalina.out contains no indication of the above error