lean_workbook_plus_68127

Open

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

Note that $\\ln(1+e^x)=\\ln\\left(e^x\\cdot\\frac{1+e^x}{e^x}\\right)=x+\\ln(1+e^{-x}).$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_68127 : ∀ x : ℝ, Real.log (1 + Real.exp x) = x + Real.log (1 + Real.exp (-x))   :=  by sorry

Source