I like this reflection by Matthew Slick of the Christian Apologetics and Research Ministry. He gives a straightforward answer to the challenge of relativism vs. absolutism:
"I was once challenged to prove that there were moral absolutes. I took up the challenge with the following argument. I asked the gentleman whether or not there were logical absolutes. For example, I asked if it was a logical absolute that something could exist and also not exist at the same time. He said, no that it was not possible.
Another example is that something cannot bring itself into existence. To this he agreed that there were indeed logical absolutes. I then asked him to explain how logical absolutes can exist if there is no God. I questioned him further by asking him to tell me how in a purely physical universe logical absolutes, which are by nature conceptual, can exist. I said, they cannot be measured, put in the test tube, weighed, nor captured; yet, they exist. So, I asked him to please tell me how these conceptual absolute truths can exist in a purely physical universe...without a God. He could not answer me.
I then went on to say that these conceptual absolutes logically must exist in the mind of an absolute God because they cannot merely reside in the properties of matter in a purely naturalistic universe. And since the logical absolutes are true everywhere all the time and they are conceptual, it would seem logical that they exist within a transcendent, omnipresent, being. If there is an absolute God with an absolute mind then he is the standard of all things as well as morals. Therefore, there would be moral absolutes.
To this argument the gentleman chuckled, said he had never heard it before, and conceded that it may be possible for moral absolutes to exist."
For more of Mr. Slick's excellent work, see www.carm.org