God works with physical and spiritual laws. Those laws follow logical rules. Therefore, reason is an excellent tool to help understand those laws.
In my opinion, you cannot have powerful faith without reason, and reason without faith is fruitless.
Good replies, however I wanted to convey a scenario that may give more depth to this Topic. For instance:
You see a dangerous situation that may affect you or your family, but your leaders tell you that regardless of that you need to be involved with the situation anyway with faith even though the most primitive of reasoning tells you that you should not.
Now you may quickly have an answer but keep in mind throughout the scriptures both Prophet and Saint were asked to do things that defy Logic. One example was Lehi leaving Jerusalem and living in the wilderness for 8 years. How many of us will be willing to do that? That is just one example. The other additive is where the source comes from. Lehi received this from God. Will you do the same if your Stake President asked? What about your Bishop? Thoughts?
I agree with NightHawk.
God's laws have a reason behind them. Why we sometimes think they defy reason or logic is because of our own inability to see the whole picture. Or because we are not quite ready for the full truth, and it is therefore hidden from us. Did you ever have the experience of learning of something new, that doesn't seem right, maybe weird, or contrary to your nature, and you study it, deeply, until you find out it's true. All of the sudden, without even maybe having found out the truth by logic but by prayer only, you all of the sudden see tons of very good reasons, and you start wondering how people could not accept it, for it was so logic, so simple, so reasonable, if they would just look? I know I have felt this way a few times.
For this discussion I think it is very important to remember what faith is, and what belief is. I think they're sometimes confused. For better understanding, I definitely recommend the Lectures on Faith. They help show the difference, and how Faith is linked to knowledge. Faith is not blind as is sometimes thought, faith is based on specific knowledge, whether from the Holy Ghost or from a text book. To kind of modernize Joseph Smith's example:
Why do you exercise in order to loose faith? You exercise because the principle in Faith on your part that excercising will result in a loss of weight leads to your action of starting to exercise. Faith is a principle of motion. You have faith that by exercising you will loose weight. It is not belief, because it's not like you just randomly exercise hoping it might do something, but because it is based on knowledge. Based on the text book knowledge for example, that excerising uses muscles. Using muscles requires ATP, which is made from ADP. To make ADP energy in the form of sugar is required. If sugar levels in the body are low enough that they are not readily available for conversion, the body will convert Fat back into sugar in order to build ATP from ADP thus enabling you to continue exercising. This is the kind of knowledge which Joseph linked to Faith.
In regards to JB's question about doing what we are told by local leaders based on Faith, I would do it if I had a knowledge of it. I don't necessarily mean that I understand it thoroughly, but that I have a sure knowledge from the LORD imparted through the Holy Spirit that what they ask me would be correct to do. Otherwise I feel I would only be doing it out of obedience, belief or simply blindness. We all have the privilege and responsibility to be guided by the Holy Spirit, and we shouldn't fail to use it.
There was a mormon publication that used to print something near the cover, I want to say I saw it in the millenial star, I wish I had it with me... I need to look it up sometime. It said something to the effect that if you could not argue the truth of your position, your position was not worth holding. I think it was a quote from an early LDS leader... As I say, I'll have to look it up and post it sometime. But yes I belief it's true, I wouldn't do something that I couldn't give a very good reason for (and to have received personal revelation from my GOD is something I consider a very good reason, as opposed to simply "because the bishop told me to").
In all cases if God tells you to do something you just do it. I will be honest here and say I do try my best to follow my leader's counsel BUT I'm not Lehi so I do go off and ponder it, pray, toss it around and whatever I need to do so when I make a secision I know it's right for my family and myself. I just don't say "Yes, bishop". Call me rebel but I like to feel sure about what I'm doing.