Theorems · Theorem · real analysis
Real.log_zpow
∀ (x : ℝ) (n : ℤ), Real.log (x ^ n) = ↑n * Real.log x
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Real.logstatement and proof · cited by 939
- Int.cast_natCastproof · cited by 393
- zpow_natCastproof · cited by 271
- zpow_negSuccproof · cited by 92
- Nat.cast_add_oneproof · cited by 56
- Real.log_invproof · cited by 35
- Int.cast_negSuccproof · cited by 32
- Real.log_powproof · cited by 29
- neg_mul_eq_neg_mulproof · cited by 20
Cited by4
Results whose statement or proof uses this declaration.
- MeromorphicOn.extract_zeros_poles_logproof · cited by 3
- AbsoluteValue.IsEquiv.log_div_log_eq_log_div_logproof · cited by 1
- Function.FactorizedRational.log_norm_meromorphicTrailingCoeffAtproof · cited by 1
- Complex.ECanonicalDecomp.log_norm_eqproof · cited by 0