DK-GEORGMOHR 1995 Problem 4

Solve the equation $(2^x-4)^3 +(4^x-2)^3=(4^x+2^x-6)^3$ where $x$ is a real number.

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.