Learn Spanish (Latin America): Pienso que vas a convencer al público con ese argumento. - I think you are going to convince the audience with that argument.

In Spanish, affirmative statements with verbs of thinking or believing (like pensar and creer) take the normal indicative mood. Even though it is your opinion, you are declaring what you believe to be a fact. You only use the subjunctive if the statement is negative, like No pienso que vayas... (I don't think you are going...).

Why is there an "al" before "público"? Is that the personal "a"?

Yes! The verb convencer (to convince) is acting on a specific group of people. Since público (audience) refers to people, it requires the personal a. When you combine the preposition a with the masculine article el, it forms the mandatory contraction al (a + el = al).

Does "público" translate to "audience" here instead of "public"?

Exactly. While el público often translates to "the public," it is also the standard Spanish word for "the audience" at a speech, play, concert, or presentation. You might sometimes see la audiencia, but el público is extremely common and natural in this context.

Why is it "ese argumento" and not "eso argumento"?