Question

Read the two excerpts from Dr. King's speech. We must come to see that no individual can live alone: no nation can live alone. *** In a real sense, we must all learn to live together as brothers, or we will all perish together as fools. What technique makes both excerpts effective

Answer 1

The technique makes both excerpts effective is an appeal to logic.
Logos is the logic, reasoning and argument, or simulation of it, in a persuasive appeal. 
Logos is a persuasive technique that tries to persuade an audience using logical arguments and supporting evidence.

Answer 2

The technique that makes both excerpts effective is appeal to logos. Logos means logic, reasoning and argument. So in order to persuade others,there must be facts that can support your argument and an intellectual information that can prove it.