Prove2Me

Lean-Workbook Plus 48665: Logarithmic identity

Proved
WorkbookRestored.plus_48665

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

lean-workbookrestored-importssource-checked

For real x,zx,z, if log⁡2x=z\log_2x=z, then log⁡x2=1/z\log_x2=1/z. Base logarithms are interpreted as Lean’s total logarithm ratios, including exceptional bases and arguments.

Source: Lean-Workbook row lean_workbook_plus_48665 (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_48665 (x z : ℝ) : Real.logb 2 x = z → Real.logb x 2 = 1 / z   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_48665; immutable original Prove2Me node 72d8dfdd-e78c-4541-8995-33de5d855b72

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