Argumentative essays (based upon facts, logos, and speaker credentials, ethos) and persuasive essays (employing pathos as well as logos and ethos) are two means of persuasion. In an argumentative essay, the primary goal is to persuade readers to take the position of the writer; therefore, it is essential to address the opposing viewpoint(s) and disabuse those of such viewpoint(s) through logical argument.
This counterargument of a persuasive essay is substantiated thoroughly with relevant facts, statistics from surveys, historical documentation, etc., statements from authorities that demonstrate and prove that the other viewpoint is not logical and sustainable.
As an example, consider one issue that was debated in the last presidential campaign: the bailing out of the American automotive industries of General Motors and Chrysler Corporation. With regard to Chrysler, for instance, if the writer of a persuasive essay were arguing, as did one presidential candidate, for Chrysler to go through bankruptcy and re-organize instead, his counterargument for not bailing this company out with government money could point to the historical facts under the Carter Administration when the first bail-out of Chrysler failed and the corporation did not make a profit, citing financial statistics as proof. He could also make the logical argument that in a capitalistic society, one that has free enterprise, the government does not own private industries such as automobile factories. So, such a bail-out is against time-honored practices of free enterprise.
If the essay is on a topic that is not one that can be supported with absolute data, then the writer must provide logical arguments that are relevant and convincing. The appeal to reason through analogy, deduction, and the like are useful. Whenever possible, the writer should try to find something in the counterargument that is a common ground for both sides, make mention of this commonality,and then launch his refutation on only the other parts. Doing this often elicits more receptive feelings from the readers.
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If one is to make an essay convincing, he or she must be sure to include researched information which supports his or her stand. In addition, statistics, facts, information that presents the counter-point and its weaknesses all help to illustrate the validity of an essay's point.
One way to look at your question is to examine it in regards to the persuasive essay. A persuasive essay is meant to persuade the audience to side with the ideology of the writer. This particular essay is meant for a supportive or a non-supportive audience. The supportive audience (reader) already agrees with the writer's point of view while the non-supportive does not. An essayist can use pathos, logos, or ethos when writing for either a non-supportive or supportive audience.
There are three types of rhetorical strategies in persuasive writing. Logos relies upon reason and logic. Ethos refers to the character, creditability, and reliability of the essayist. Pathos is the emotional appeal which takes into consideration the values and needs of the audience.
The persuasive essayist must be especially concerned with the wavering or hostile audience. These are the two types of audience which most need persuasion. The wavering audience may have some interest in the topic argued, yet they may not necessarily believe what the essayist has to say about the subject while the hostile audience, on the other hand, is typically negative towards either the topic or the essayist. The essayist wants to provide solid, verifiable, and convincing information and use all three strategies (logos, pathos, and ethos) to appeal to the audience. The essayist must additionally prove his or her reliability and use all three strategies to help the audience identify the reason and conviction in the essay.