How can I convert a logo to a single lighter colour in Illustrator or Photoshop?

I'd like to convert some client logos into a single light grey colour #BFBFBF

The logos are in png and jpeg formats on a white background.

I know that I can convert the image to greyscale and / or use the channel mixer but it's not giving me the exact colour I need.

Example logo:

Everything the isn't white needs to be #BFBFBF