The use of logical arguments and hard facts to show the target that the request is a worthwhile one is called:

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Rational persuasion involves using logical arguments and hard facts to show the target that the request is a worthwhile one. Ingratiation is using flattery or fawning to influence a target, consultation is seeking input or advice from a target, collaboration involves working together on a mutually beneficial goal, and inspirational appeal involves appealing to a target's emotions or values.

The Use of Logical Arguments and Hard Facts to Show