Using Graduated Neutral Density Filters
These filters aren't just for taming overly bright backgrounds. I also use them to brighten up dark foregrounds. It's really the same concept as the Mt. Rainier example it just looks opposite. I'm still placing the dark part of the filter over the brightest part of the scene, allowing my camera to capture the entire range of light. This was probably done with a three-stop filter.
On a side note, it looks like balancing the exposure with the filter also affected the white balance. Both of these images were photographed using Auto White Balance in the camera and are shown "as shot" without any Lightroom or Photoshop adjustments. The color in the "Before" image is probably more accurate, but I find the color in the "After" image more pleasing.
For a more detailed explanation of how to choose and use GND filters, read my article in the Articles section of this site.
Grab the slider and move it left and right to see the difference.