No, this isn't logged presently. It'll be logged *THAT* such a task has been started, but we don't log presently who did it.
At least, not if it's a public task (you can at best stand a chance to find who OWNS the task, but that doesn't necessarily mean that they're the one who started it).
There may have been an ER for this ... either way, you'll want to get in touch with LANDesk support and log this as an enhancement request. .
- Paul Hoffmann
LANDesk EMEA Technical Lead