lean_workbook_plus_3995

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

Note that $\log_{10}2\approx0.301$ , so $2^{100}\approx\left(10^{0.301}\right)^{100}=10^{(0.301)(100)}=10^{30.1}$ , and thus $10^{30}<10^{30.1}\approx2^{100}<10^{31}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_3995 :
  (10:ℝ)^30 < 2^100 ∧ 2^100 < (10:ℝ)^31   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook

View graph