Real logarithm identity #27624

Proved

WorkbookCorrected.plus_27624

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

arithmeticcorrectedelementaryworkbook

The elementary natural-number / rational identity

(Real.logb 2 3) * (Real.logb 3 4) * (Real.logb 4 5) * (Real.logb 5 6) = Real.logb 2 6

holds by direct arithmetic evaluation.

Formalization Note: This corrects Lean-Workbook record lean_workbook_plus_27624, 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_27624 (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_27624 : (Real.logb 2 3) * (Real.logb 3 4) * (Real.logb 4 5) * (Real.logb 5 6) = Real.logb 2 6 := by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook; record lean_workbook_plus_27624; Apache-2.0; corrects Open node 533ec740-f80c-4d30-938c-7f9fd8382698

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