Comparing two large powers using small bases

Proved

WorkbookSource.problem_7831

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Which is bigger, $2^{3000}$ or $3^{2000}$ ? Assume no calculators and no logarithm tables.

Source: InternLM Lean-Workbook, record lean_workbook_7831 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_7831 : (2^3000:ℝ) < 3^2000  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_7831; Apache-2.0

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