I have 3 lbs of butter that has been left at room temperature since, about, December 22nd. Is it still safe to eat?
I'm only speaking from my own experience. I am no authority on the topic of butter, but I do have some experience with it left at room temperature for good amounts of time.
When I was growing up, my parents would always leave butter at room temperature. Although, it was about one pound at a time. Refrigerated butter is unpleasant because it is so hard it can't be spread very well, by the time the butter melted enough to spread, your toast is cold. So we left it out and nobody ever got sick from it.
Here are some facts about the composition of butter, based on this WebExhibits page:
Commercial butter is 80–82 percent milk fat, 16–17 percent water, and 1–2 percent milk solids other than fat (sometimes referred to as curd). It may contain salt , added directly to the butter in concentrations of 1 to 2 percent.
So we have established it is mostly milk fat, and 1-2% salt. Now here is an excerpt from a microbiology article about butter:
Salting effectively controls bacterial growth in butter. The salt must be evenly dispersed and worked in well. Salt concentration of 2% adequately dispersed in butter of 16% moisture will result in a 12.5% salt solution throughout the water-in-oil emulsion.
I'm going to go to an article on Chow.com about the topic:
If your butter tastes stale, bitter, and has a strong smell, it’s probably rancid. Rancidity is the result of the fat oxidizing. This process is accelerated by exposure to light, heat, and contact with certain metals (for instance, in utensils).
That said, the California Milk Advisory Board recommends keeping butter wrapped and stored in the coldest part of the refrigerator for optimal freshness and flavor, and to keep it from picking up unwanted odors.
Potential good news
I've also been browsing an article on EatByDate.com which seems to indicate that the primary effect of leaving butter at room temperature is:
Can You Store Butter on the Counter?
Commercially prepared butter can safely be stored on the counter, however, it is not recommended if your intent is to extend its shelf life and freshness. Butter is like a sponge, it absorbs the odors from surrounding foods quite easily and this will affect its taste. If you are storing butter on the counter we recommend keeping it in a tightly sealed container to block odors and bacteria. The butter will last for several days at a temperature of 65 degrees Fahrenheit.
TL; DR: Play it safe
If there are any signs of sourness, any unusual smells, any sign of mold, better toss it. Otherwise, consume at your own risk. We can't give any kind of authoritative answers as to whether your butter is still OK, as there are so many variables involved that we can't know about. (and we're not microbiologists)