A product of four successive real exponents

Proved

WorkbookRestored.plus_3309

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

lean-workbookrestored-importssource-checked

Let $a,b,c,d$ be real numbers satisfying $4^a=5$ , $5^b=6$ , $6^c=7$ , and $7^d=8$ . Then

abcd=\frac32.

This restores the missing imports or namespaces of the original node, retaining its formal proposition. Source: Lean-Workbook row lean_workbook_plus_3309 (Apache-2.0).

Preamble

import Mathlib.Analysis.SpecialFunctions.Pow.Real
import Mathlib.Analysis.SpecialFunctions.Log.Base
open Real

Formal statement

theorem WorkbookRestored.plus_3309 (a b c d : ℝ) (h1 : (4:ℝ)^a = 5) (h2 : (5:ℝ)^b = 6) (h3 : (6:ℝ)^c = 7) (h4 : (7:ℝ)^d = 8) : a*b*c*d = 3/2   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_3309; original Prove2Me node 4ecbede2-e1ae-48fd-8918-9af11144d4de; Apache-2.0

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