The goal of database mirroring is to keep two databases synchronized in near real-time for High Availability/Disaster Recover (HA/DR) purposes and the mechanism to achieve that is as Perry states.

It's true that a form of disaster prevention can be gained via Log Shipping because you can configure the lag between transaction log backups being taken on the Primary and being restored on the Secondary so if someone dropped a table on the Primary you'd have a chance of preventing that table being dropped on the Secondary, but the longer that lag period is, the less suitable Log Shipping is as a HA/DR solution.

What perceived benefit of Log Shipping are you hoping to realize through the use of Database Mirroring?

Regards

Lempster