Real logarithm identity #4340

Proved

WorkbookCorrected.plus_4340

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

arithmeticcorrectedelementaryworkbook

The elementary natural-number / rational identity

Real.logb 3 (2^102) = 102 * Real.logb 3 2

holds by direct arithmetic evaluation.

Formalization Note: This corrects Lean-Workbook record lean_workbook_plus_4340, 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_4340 (Apache-2.0).

Preamble

import Mathlib.Data.Real.Basic
import Mathlib.Analysis.SpecialFunctions.Log.Base
import Mathlib.Tactic.Ring
import Mathlib.Tactic.Positivity
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.NormNum

Formal statement

theorem WorkbookCorrected.plus_4340 : Real.logb 3 (2 ^ 102) = 102 * Real.logb 3 2 := by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook; record lean_workbook_plus_4340; Apache-2.0; corrects Open node 41bef039-b73a-4868-ab12-7fd1ddf8ebc2

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