Lean-Workbook Plus 9408: Logarithmic inequality

Proved

WorkbookRestored.plus_9408

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

lean-workbookrestored-importssource-checked

If $x>0$ and $x\ne1$ , then $x^{\log 30/\log x}=30$ , where the exponent is real.

Source: Lean-Workbook row lean_workbook_plus_9408 (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_9408 (x : ℝ) (hx : x > 0 ∧ x ≠ 1) : x^((Real.log 30) / (Real.log x)) = 30   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_9408; immutable original Prove2Me node ddc40de1-4754-47b3-a386-987cf13ed947

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