Real logarithm identity #59593

Proved

WorkbookCorrected.plus_59593

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

arithmeticcorrectedelementaryworkbook

The elementary natural-number / rational identity

(5 * Real.logb 3 2 + 2 * Real.logb 9 10) = (6 * Real.logb 3 2 + Real.logb 3 5)

holds by direct arithmetic evaluation.

Formalization Note: This corrects Lean-Workbook record lean_workbook_plus_59593, 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_59593 (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_59593 : (5 * Real.logb 3 2 + 2 * Real.logb 9 10) = (6 * Real.logb 3 2 + Real.logb 3 5) := by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook; record lean_workbook_plus_59593; Apache-2.0; corrects Open node e8d6f638-cde6-4ba5-accd-fd7562dfbeff

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