Prove2Me

Multiplying two logarithmic change-of-base ratios

Proved
WorkbookRestored.plus_2050

by wamlart · Sep 12, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

lean-workbookrestored-importssource-checked

The natural logarithm ratios satisfy

log⁡5log⁡3log⁡7log⁡5=log⁡7log⁡3.\frac{\log5}{\log3}\frac{\log7}{\log5}=\frac{\log7}{\log3}.

Formalization Note This restores source entry lean_workbook_plus_2050 from the Apache-2.0 Lean-Workbook dataset. The mathematical proposition is unchanged; targeted imports and namespace openings supply the constants missing from the original Prove2Me node 931776e9-cc1e-4b80-9a4e-f2428c2875fb. This is a separate corrected node because formal statements and preambles are immutable.

Preamble
import Mathlib.Analysis.SpecialFunctions.Log.Base
import Mathlib.Tactic
open Real
Formal statement
theorem WorkbookRestored.plus_2050 : Real.log 5 / Real.log 3 * (Real.log 7 / Real.log 5) = Real.log 7 / Real.log 3   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_2050; original Prove2Me theorem ID 931776e9-cc1e-4b80-9a4e-f2428c2875fb; Apache-2.0.

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