CONO-SUR 1998 Problem 3

Prove that, least $30$ % of the natural numbers $n$ between $1$ and $1000000$ the first digit of $2^n$ is $1$ .

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.