Some log homes have very steep roofs.  They can be so steep that they almost look like an A-Frame building.  Other log homes have shallower roof pitches.  More like what you might see in typical modern stick frame construction.  There are some reasons why a shallow roof pitch is easier and less expensive to build and work on, versus a steep roof pitch.  Here are 4 of the reasons:

• Steep roofs are harder to work on. Usually you have to install roof jacks so you have someplace to stand.  Wearing a safety harness becomes mandatory rather than optional.  That's two extra steps that you have to take on steep roofs that normally aren't required on more shallow roofs, and extra steps means extra time money.  Here's an example of a very steep roof with temporary roof jacks installed:

• Steep roofs end up using more building materials to cover the same horizontal distance, as opposed to shallow roofs.  That's because as the angle of your roof increases, the length of your rafters increase.  As the length of your rafters increase, the surface are of your roof increases.  That means you will need to buy more sub roof materials, insulation, roofing material, et cetera for roofs with steeper pitches.  Obviously the more materials you have to buy and install, the more expensive and lengthy your project becomes -- and it also becomes less environmentally friendly because you are consuming more raw materials.

• Steep roofs can contribute to higher heating costs.  The basic issue is that heat rises.  With a steep roof the peak of your roof is very high, which means all the hot air in your log home will end up filling the giant cathedral ceiling made by your steep roof.  It is much more energy efficient to have a more shallow roof pitch, and thus more eco-friendly since you'll use less fuel to heat your log home.
• Steep roof pitches also make the eaves of your log home angle sharply down in relationship to your exterior walls.  That can result in a situation where you look out your windows and see nothing but the underside of your own roof.  While looking at the underside of your roof occasionally can be nice, having it be the only 'view' from inside your home isn't the most esthetically pleasing experience.  Here's an example of the issue (note that you shouldn't just cut the eaves shorter on the steep roof because you would lose water protection for the logs):

Steep roofs do have a potential advantage.  They tend to shed snow more effectively than shallow roofs.  That can be useful if you're building up in the mountains, and have lots of snow to deal with.

In most situations though, a shallow roof pitch is by far the best option.  6/12 is about as steep as most builders would want to go (6 inches rise per every 12" horizontal run).  Shallow roofs will generally be less expensive to build, easier to build, quicker to build, use less raw materials, and be more energy efficient. 

At our 2 day log home class we fully explain the roofing process.  Our students end up with an excellent understanding of the above roofing issues and many, many more.