logb_div_base — Mathlib

English

Logarithm of a quotient base relation: log_b(a/b) c = ((log_b a c)^{-1} − (log_b b c)^{-1})^{-1}.

Русский

Логарифм от частного по основанию: log_b(a/b) c = ((log_b a c)^{-1} − (log_b b c)^{-1})^{-1}.

LaTeX

$$$\log_b\left(\frac{a}{b}\right) c = \left( (\log_b a c)^{-1} - (\log_b b c)^{-1} \right)^{-1}$$$

Lean4

theorem logb_div_base {a b : ℝ} (h₁ : a ≠ 0) (h₂ : b ≠ 0) (c : ℝ) : logb (a / b) c = ((logb a c)⁻¹ - (logb b c)⁻¹)⁻¹ :=
  by rw [← inv_logb_div_base h₁ h₂ c, inv_inv]

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