Display logs and last change on LTM via automation !!

Simply put, BIG-IP dumps information to syslog (local and/or remote) and generates SNMP data. You can configure it to log as much or as little as you want, and event be somewhat specific about what you log. But it does not have the built-in log correlation and filtering functions that you may be looking for. You either need to acquire such a product, or build scripts to do the filtering on the box (bash, grep, sed, awk, etc.).