Theorems · Theorem · real analysis
Real.log_rpow
∀ {x : ℝ}, 0 < x → ∀ (y : ℝ), Real.log (x ^ y) = y * Real.log x- Cited by
- 31 results in Mathlib
- Foundations
- Depth 196 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- mul_commproof · cited by 2,262
- Real.logstatement and proof · cited by 939
- Real.expproof · cited by 871
- Real.exp_posproof · cited by 169
- Real.rpow_pos_of_posproof · cited by 155
- Real.exp_logproof · cited by 58
- Real.rpow_def_of_posproof · cited by 35
- Real.exp_injectiveproof · cited by 12
Cited by31
Results whose statement or proof uses this declaration.
- Real.lt_rpow_iff_log_ltproof · cited by 5
- Real.convexOn_log_Gammaproof · cited by 5
- Real.logb_rpowproof · cited by 5
- Real.le_rpow_iff_log_leproof · cited by 4
- ENNReal.log_rpowproof · cited by 4
- Real.rpow_le_rpow_left_iffproof · cited by 4
- Real.rpow_le_rpow_left_iff_of_base_lt_oneproof · cited by 4
- isLittleO_log_rpow_atTopproof · cited by 3
- Real.log_le_rpow_divproof · cited by 2
- Real.rpow_le_iff_le_logproof · cited by 2
- tendsto_rpow_div_mul_addproof · cited by 2
- Real.rpow_logb_eq_absproof · cited by 2