I once completely ascribed to the LDS notion that the Trinity just didn't make sense. How could one being be three? How could God just be a blob of Spirit or Light or something immaterial? Didn't that limit who and what he was? Why would he say we were made in his image if we weren't?
Well, amazingly, the Trinity can be correct--and it is Biblical--without flying in the face of those questions.
First of all, let's look at the simple reasoning that if there is only one God, then Jesus had to either be God or not be divine at all. Isaiah 43:10 and 44:6, 8 establish this very well. Notice how definite God is:
Before me no god was formed,
nor will there be one after me.
I am the first and I am the last;
apart from me there is no God.
Is there any God besides me?
No, there is no other Rock; I know not one.
Now, if you accept there is only one God, then you have to ask if Jesus was divine. First of all, the heresy that he was not divine was originally called Arianism, and fighting that heresy is the reason that the doctrine of the Trinity was established so firmly. Also, how else could a human be perfect? We were sinful by nature: it is impossible for us to be completely perfect as creations with free will and a knowledge of good and evil which allows us to use that fee will to sin. Furthermore, a mere human couldn't break the bonds of death for everyone and take on the sins of the world for all.
There are many verses that support Jesus being God, including John 1:1,14 and the last few verses of John 8 (Christ identifies himself as "I am," as God does in the burning bush in Exodus), and many others.
It was not in God's physical image that we were made, but in his spiritual image. Before Joseph Smith tampered with the verse, John 4:24 read:
"God is spirit, and his worshipers must worship in spirit and in truth."
Furthermore, we are made up of multiple parts: just consider the separation of body and spirit upon our deaths. I've also been told that our soul is our third part, but I'm not educated upon that aspect, so I can only give so much. I can say, though, that it makes us very much like God indeed: God and our spirit are comparable, Jesus and our bodies are comparable, and the Holy Spirit and perhaps our souls are comparable. We are as triune in nature as God.
I would urge any curious LDS reader to study deeply in the scriptures on whether or not the Trinity is supported within the precious pages. And for those who would say it can't be doctrine because it isn't expressly said in the verses: remember, "monotheism" isn't expressly said either.