The Logical Argument was proposed by Jonathan Sarfati, B.Sc. (Hons.) in Chemistry (with condensed matter and nuclear physics papers substituted) and Ph.D. in Spectroscopy (Physical Chemistry). He put forward the Logical Argument for the universe’s existence in April 1998 as:
Everything which has a beginning has a cause.
The universe has a beginning.
Therefore the universe has a cause.
There is logical evidence that the universe had a beginning. This can be shown from the Laws of Thermodynamics, the most fundamental laws of the physical sciences and the supposed echo left over from the Big Bang (Creation?). Sarfati’s proposal uses established scientific knowledge to validate his argument like in the Laws of Thermodynamics.
1st Law: The total amount of mass-energy in the universe is constant.
2nd Law: The amount of energy available for work is running out, or entropy is increasing exponentially. Since the total amount of mass-energy is limited, and the amount of usable energy is decreasing (running out), then the universe can not have existed forever, otherwise it would already have exhausted all usable energy by now. When all usable energy is used, then what is called the ‘heat death’ of the universe will occur. For example, all radioactive atoms would have decayed, every part of the universe would be the same temperature, and no further work would be possible.
So the obvious corollary is that the universe began a finite time ago with a lot of usable energy, and is now running down. Running down implies a beginning. A wood match will quickly burn the sulfur but it will never break down so much as to be recycled into creating sulfur again. This is the same reason that there can be no Steady State theory; one in which the universe has always existed. Or that it is eternally recycled every trillions years or so. You can recycle aluminum cans but you can never retrieve the original elements, heat, or energy. It’s a one way process. I can’t retrieve or recycle the light that our lamp has put out last night and put in back into the bulb or the electrical system. The same applies to star light; light that has already pierced deep into the edges (or beyond?) of the universe, which can n ever be put back to where it came from or recycled by a collapsing universe. Kinetic energy used is kinetic energy spent.
It is self-evident that things that have a beginning also have an ending. The law of cause and effect provides that the universe could not be self-caused, or created itself. Nothing can create itself without an outside cause, at least equal to or greater than itself. To say the universe (& matter) had no cause, caused itself or has always existed, is essentially saying that all matter existed before it came into existence, which is a logical absurdity. And if there must have been something there to cause nothing to bring into existence something, then logically there was not nothing there, but had to be something that made something happen.
Dr. R.C. Sproul, an extraordinary Theologian and Philosopher (Ligonier Ministries), can put it so much better than I . He was quoted by John McArthur (gracetoyou.org) as saying that only four options for the origin of the universe are possible.
“Option number one, the universe is an illusion, it doesn’t exist.
Option number two, it is self-created.
Option number three, it is self-existent and eternal.
Option four, it was created by someone who is self-existent.” 
There are no other options. Either it doesn’t exist or it created itself, or it always existed, or somebody created it. That’s it. Dr. Spoul says that “I have puzzled over this for decades and sought the counsel of philosophers, theologians and scientists. I have been unable to locate any other theoretical options that cannot be subsumed under these four options. That’s all you’ve got.” 
Then Dr. Sproul says, “Option number one must be eliminated for two reasons.” That’s the option that says it doesn’t exist, it’s all an illusion. “First, if it’s a false illusion, then it isn’t an illusion. If it’s a true illusion, then someone or something must be existing to have that illusion. If this is the case then that which is having the illusion must either be self-created, self-existent, or caused by someone ultimately self-existent. So therefore everything is not an illusion.”  If we assume the illusion is absolute and that nothing does exist, including that which is having the illusion, then there is no question of origins even to answer because literally nothing exists.
The second option is that the universe created itself, which by all logic is formally false. It is both contradictory and logically impossible. Dr. Sproul argues that, “In essence, self-creation requires the existence of something before it exists.”  What Dr. Sproul is saying that the universe can’t create itself unless it first existed to be able to create itself. In that case you could ask, “What caused the universe to create itself? It would had to have a greater cause outside of itself, which in case meant it must have had a cause or creator.
Dr. Sproul says a self-created universe is “…a logical and rational impossibility,” and “for something to create itself it must be before it is. This is impossible…it’s impossible for solids, liquids and gases, it’s impossible for atoms and subatomic particles, it is impossible for light, it is impossible for heat, it is impossible for God. Nothing anywhere any time can create itself because if it could it would have to exist before it created itself.”  Sproul points out that in it he can be self-existent and not violate logic, but it can’t be self-created.
Whether it is the Big Bang theory, scientists are essentially saying that nothing exploded into something, which is a logical impossibility. To retain a theory of self-creation is totally irrational and rejects all logic. Such a theory can be believed but it can’t be argued reasonably and can never be established as a fact.
The third option that Dr. Sproul mentions is that the universe has always existed eternally. The Steady State theory states that the universe has always existed., and there was not a time when matter did not exist. But the major problem with this is that everything we see or know of in the entire universe has a beginning and an ending. Planets, plant life, human life, suns…even gigantic galaxies. There is nothing materially eternal in the universe. I once didn’t exist, the house I live in….everything there is at one time did not exist, and if it exists now, it will cease to exist in time. There are all kinds of things in this world that once did not exist but do now and things that once did, that no longer exist today. Nothing can be born and have always existed.
1. Sproul, Dr. R. C., Defending Your Faith. Excerpts from John McArthur. Copyright 2009. http://www.gty.org/Resources/Sermons/90-216
An excerpt from Chapter Six of “Blind Chance or Intelligent Design?, Empirical Methodologies and the Bible”, by Jack Wellman. Copyright 2009.