I just downloaded the newest version of Solr from http://www.eu.apache.org/dist/lucene/solr/5.3.1/solr-5.3.1.tgz
Then I unpacked it with tar zxvf solr-5.3.1.tgz
I don't think the log file is being deleted - it's probably just never created. Solr and Lucene 5.3 require Java 7, so if the Java6 VM is the JVM used for starting Solr - it's going to fail.
You can use ./solr start -f
to get Solr to run in the foreground to catch any errors, but if the logging sub system never starts, it might not do much good.