Lean-Workbook Plus 44381: Logarithmic identity

Proved

WorkbookRestored.plus_44381

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

lean-workbookrestored-importssource-checked

If $x=2^{\log_6 18}3^{\log_6 3}$ , then $x=6$ , with real powers.

Source: Lean-Workbook row lean_workbook_plus_44381 (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_44381 (x : ℝ) (hx : x = 2^Real.logb 6 18 * 3^Real.logb 6 3) : x = 6   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_44381; immutable original Prove2Me node 87219995-cee1-410f-812c-3c28b289155c

View graph