AMC's log Export function exports only messages that are currently being viewed/displayed in AMC, and not the entire log file, as described in the Installation and Administration Guide and online AMC help:
[Snippet from the admin guide]
This is a documentation error and the current behavior is by design. AMC allows an administrator to export the log file based on the search criteria displayed in the AMC. The administration guide will be updated to reflect this in appliance release 10.5.0.