Real logarithm identity #29456

Proved

WorkbookCorrected.plus_29456

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

arithmeticcorrectedelementaryworkbook

The elementary natural-number / rational identity

Real.logb 3 (90 - 3^4) * Real.logb 2 (76 - 44) * Real.logb 6 (1421 - 5^3) = 40

holds by direct arithmetic evaluation.

Formalization Note: This corrects Lean-Workbook record lean_workbook_plus_29456, 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_29456 (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_29456 : Real.logb 3 (90 - 3 ^ 4) * Real.logb 2 (76 - 44) * Real.logb 6 (1421 - 5 ^ 3) = 40 := by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook; record lean_workbook_plus_29456; Apache-2.0; corrects Open node 4b1ff3db-76bc-4e00-adfa-076a4ed651d5

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