A cross-product identity for logarithm quotients

Proved

WorkbookSource.problem_22623

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Prove the logarithmic identity: $\left(\log_{a}b\right)\left(\log_{c}d\right)=\left(\log_{a}d\right)\left(\log_cb\right)$

Source: InternLM Lean-Workbook, record lean_workbook_22623 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_22623 (a b c d : ℝ) : (Real.log b / Real.log a) * (Real.log d / Real.log c) = (Real.log d / Real.log a) * (Real.log b / Real.log c)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_22623; Apache-2.0

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