Real logarithm identity #22147

Proved

WorkbookCorrected.plus_22147

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

arithmeticcorrectedelementaryworkbook

The elementary natural-number / rational identity

Real.logb 25 10 = Real.log 10 / Real.log 25

holds by direct arithmetic evaluation.

Formalization Note: This corrects Lean-Workbook record lean_workbook_plus_22147, 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_22147 (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_22147 : Real.logb 25 10 = Real.log 10 / Real.log 25 := by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook; record lean_workbook_plus_22147; Apache-2.0; corrects Open node a3758ce7-7b1c-4fb4-87d1-4d0c24212a11

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