Prove2Me

Lean-Workbook Plus 34341: Logarithmic inequality

Proved
WorkbookRestored.plus_34341

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

lean-workbookrestored-importssource-checked

For positive real a,b,ca,b,c, log⁡ab+log⁡ac=log⁡a(bc)\log_a b+\log_a c=\log_a(bc). The base logarithm is Lean’s total ratio log⁡t/log⁡a\log t/\log a, including at a=1a=1.

Source: Lean-Workbook row lean_workbook_plus_34341 (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_34341 : ∀ a b c : ℝ, a > 0 ∧ b > 0 ∧ c > 0 → Real.logb a b + Real.logb a c = Real.logb a (b * c)   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_34341; immutable original Prove2Me node 17fbcfec-676d-481e-930b-2e4bf34d5ee0

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