Lean-Workbook Plus 36143: Logarithmic inequality

Proved

WorkbookRestored.plus_36143

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

lean-workbookrestored-importssource-checked

For real $a$ and $x>0$ , $a\log x=\log(x^a)$ , with real exponentiation. This is the first identity in the source.

Source: Lean-Workbook row lean_workbook_plus_36143 (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_36143 (a x : ℝ) (h₁ : x > 0) : a * Real.log x = Real.log (x ^ a)   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_36143; immutable original Prove2Me node 940879bb-cdcb-44e1-bdbe-818401839e7d

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