CMOQR 2013 Problem 1

Determine all real solutions to the following equation: $2^{(2^x)}-3\cdot2^{(2^{x-1}+1)}+8=0.$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.