Prove2Me

Lean-Workbook Plus 54693: Logarithmic identity

Proved
WorkbookRestored.plus_54693

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

lean-workbookrestored-importssource-checked

∑j=261/log⁡j(1/7)−∑j=7101/log⁡j(1/7)=1\sum_{j=2}^{6}1/\log_j(1/7)-\sum_{j=7}^{10}1/\log_j(1/7)=1. The formal statement writes out these nine terms explicitly.

Source: Lean-Workbook row lean_workbook_plus_54693 (Apache-2.0). The unchanged proposition comes from the original record; its missing mathematical imports and namespaces are restored here.

Preamble
import Mathlib.Analysis.SpecialFunctions.Log.Base
open Real
Formal statement
theorem WorkbookRestored.plus_54693 :
  (1 / Real.logb 2 (1 / 7)) + (1 / Real.logb 3 (1 / 7)) + (1 / Real.logb 4 (1 / 7)) + (1 / Real.logb 5 (1 / 7)) + (1 / Real.logb 6 (1 / 7)) - (1 / Real.logb 7 (1 / 7)) - (1 / Real.logb 8 (1 / 7)) - (1 / Real.logb 9 (1 / 7)) - (1 / Real.logb 10 (1 / 7)) = 1   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_54693; immutable original Prove2Me node 2fbc9765-e529-4dfa-912c-ef64cc2cef80

View graph