How do I update a dark log home?

What kind of lighting do you use? Are you using natural spectrum light? They are available in spiral fluorescent bulbs and LEDs. Natural spectrum are a cool bright (blue) light in comparison to the warm (orangy hued) lights. May take a bit to get used to.

Yes we have those throughout our home. I've even sheet rocked the interior walls and painted a light taupe but it still looks like a dungeon in here.

I feel your pain. My living room is dark all the time.

mirrors.

A skylight or those solartubes would help if the home is one floor. I have a skylight and it makes a huge difference.

PAINT, PAINT, PAINT!!!

Apply Kilz first so you have no "bleed through". Ask at a specialty paint store if they recommend also putting on a coat of primer after the Kilz. Since you've been living in the dark ages for ages, you may want to paint everything white at first so you can get used to it. From there, you can begin to bring color into your home. Try to stick with "cool" hues and lighter tones such as sherbet type colors.

Even with the color "white", there a zillion variations. You can begin to learn about cool vs warm hues starting with the white you choose. Take a piece of printer paper to the paint store with you. Printer paper tends to come in "white" ranging from anything like 75-98% pure. Take the "whitest" paper you can get your hands on!

At the store, just pull out some color strips of white. Hold them against your printer paper and you'll instantly see that some have yellow undertones, some have blue undertones, some have silver. Once you can see those differences, you start getting the idea of warm vs cool. A white with yellow tones is warm and will start becoming a beige-like white in your home. However, a white with silver undertones is a cool color. It works well with a cool gray, some shades of blue or green etc. Paint your ceiling "ceiling white" which is very white. I'd recommend you then paint the walls a cool white and live with it for awhile.

Here is an explanation of cool colors. These are pretty much the colors I prefer. They make my spaces feel "airy" and don't drag your eyes to anything other than those I purposely make stand out.

https://www.thespruce.com/understanding-warm-and-cool-colors-1976480