Real logarithm identity #18935

Proved

WorkbookCorrected.plus_18935

by carlok · Sep 30, 2026 · Mathlib 0df444a (Lean v4.33.1)

arithmeticcorrectedelementaryworkbook

The elementary natural-number / rational identity

(Real.logb 2 (4 * 251)) / (Real.logb 2 (2 * 5)) = (2 + Real.logb 2 251) / (1 + Real.logb 2 5)

holds by direct arithmetic evaluation.

Formalization Note: This corrects Lean-Workbook record lean_workbook_plus_18935, which omitted a compilable colon/type annotation and/or used a preamble of only Mathlib.Analysis.Complex.Basic.

Source: InternLM Lean-Workbook, record lean_workbook_plus_18935 (Apache-2.0).

Preamble

import Mathlib.Data.Real.Basic
import Mathlib.Analysis.SpecialFunctions.Log.Base
import Mathlib.Analysis.SpecialFunctions.Log.Basic
import Mathlib.Tactic.Ring
import Mathlib.Tactic.FieldSimp
import Mathlib.Tactic.Positivity
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.NormNum

Formal statement

theorem WorkbookCorrected.plus_18935 : (Real.logb 2 (4 * 251)) / (Real.logb 2 (2 * 5)) = (2 + Real.logb 2 251) / (1 + Real.logb 2 5) := by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook; record lean_workbook_plus_18935; Apache-2.0; corrects Open node 2e5720e5-fb54-4997-ba9f-941a454d8d46

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