Real logarithm identity #30757

Proved

WorkbookCorrected.plus_30757

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

arithmeticcorrectedelementaryworkbook

The elementary natural-number / rational identity

(Real.logb 2 9) * (Real.logb 3 7) * (Real.logb 7 8) = 6

holds by direct arithmetic evaluation.

Formalization Note: This corrects Lean-Workbook record lean_workbook_plus_30757, 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_30757 (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_30757 : (Real.logb 2 9) * (Real.logb 3 7) * (Real.logb 7 8) = 6 := by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook; record lean_workbook_plus_30757; Apache-2.0; corrects Open node 435ce9cc-c79a-4bf9-abcf-d780bde8af8b

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