Theorems · Theorem · real analysis
Real.log_pow
∀ (x : ℝ) (n : ℕ), Real.log (x ^ n) = ↑n * Real.log x
- Cited by
- 29 results in Mathlib
- Foundations
- Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
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
- one_mulproof · cited by 2,841
- Nat.cast_oneproof · cited by 2,501
- MulZeroClass.mul_zeroproof · cited by 2,091
- MulZeroClass.zero_mulproof · cited by 1,625
- eq_or_neproof · cited by 1,117
- pow_zeroproof · cited by 1,094
- Real.logstatement and proof · cited by 939
- Nat.cast_addproof · cited by 586
- pow_succproof · cited by 374
- add_mulproof · cited by 363
- zero_powproof · cited by 361
Cited by29
Results whose statement or proof uses this declaration.
- Real.log_sqrtproof · cited by 5
- Chebyshev.theta_le_log4_mul_xproof · cited by 4
- Real.log_zpowproof · cited by 4
- Chebyshev.psi_geproof · cited by 3
- NumberField.mixedEmbedding.fundamentalCone.sum_expMap_symm_applyproof · cited by 2
- ArithmeticFunction.vonMangoldt_sumproof · cited by 2
- Chebyshev.sum_PrimePow_eq_sum_sum'proof · cited by 2
- NumberField.Units.sum_mult_mul_logproof · cited by 2
- Chebyshev.abs_psi_sub_theta_le_sqrt_mul_logproof · cited by 2
- Complex.log_inv_eq_iteproof · cited by 2
- Real.Gamma_three_div_two_lt_oneproof · cited by 2
- Stirling.log_stirlingSeq_formulaproof · cited by 1