How do I write an essay that is objective but is persuasive?

Really depends on what the subject is.
As you have given us scant information it will be very difficult to help you.

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There's a short checklist of things to do to write an objective persuasive essay:

1. Identify your topic. Chances are, you've already done this, or had it done for you.
2. Identify the various sides of the topic. You don't have to be entirely thorough (in an essay on whether the bread should be butter side up or butter side down, you don't absolutely have to cover grape jelly), but any major faction should be represented.
3. Research a few of the main points in favor of each side of the topic. Try to make sure that you have comparable points for the sides, as this will make the entire essay come together better.
4. Choose which side you want to argue for. This can be done at any point between choosing the topic and writing the conclusion, really, but this is the most efficient time to do it.
5. Write a paragraph for each set of complementary points, trying to urge your reader along to your chosen side. Be fair and evenhanded about that part, though.
6. String the paragraphs together in your preferred essay form.
7. Write up your introduction and conclusion.

It can be a lot of work, especially if you have a complicated topic, but it's much easier to attack the problem in this order (or any other rational order, really, but this is one that's worked for me in the past)