You can build a log cabin on your land.
However the process of building a log cabin on your land will depend on your where your land is and whether or not you need any permits and if your area requires compliance with building codes.
If building in a town or municipality or a county that requires permits you would need to get the necessary building permits and build the log cabin to comply with any building codes.
In some locations, environmental impact assessments and site inspections are also sometimes required.
Also you have to consider on whether the log cabin is being tied into city water and sewer or with a well and septic.
If installing a septic you often need a perc test done to ensure the septic drain field can drain off the water correctly and fast enough.
In some locations you may be able to build the log cabin without any permits if you're way out in the woods somewhere.
I've known a few people that own several acres of wooded land and they build log cabins out there on their properties without getting any permits and they've been just fine.
However in some locations they may find that you built the log cabin or other building without a permit and may even order it to be torn down.
So you would have to fully check with your county, town etc about any zoning issues or any permits that may be needed if you're in town or close to town.
But way out in the woods you may be able to get by without the permits and zoning issues.