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Theorems · Theorem · real analysis

ENNReal.log_pow

∀ {x : ENNReal} {n : ℕ}, (x ^ n).log = ↑n * x.log
Defined in
Mathlib.Analysis.SpecialFunctions.Log.ENNRealLog
Cited by
3 results in Mathlib
Foundations
Depth 205 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

ExpGrowth.expGrowthSup_pow · cited by 1ExpGrowth.expGrowthSup_powEReal.exp_nmul · cited by 0EReal.exp_nmulExpGrowth.expGrowthInf_pow · cited by 0ExpGrowth.expGrowthInf_powENNReal · cited by 9879ENNRealEReal · cited by 793ERealENNReal.log · cited by 72ENNReal.logENNReal.rpow_natCast · cited by 18ENNReal.rpow_natCastENNReal.log_rpow · cited by 4ENNReal.log_rpowEReal.coe_natCast · cited by 1EReal.coe_natCastENNReal.log_powCITED BYCITES

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by3

Results whose statement or proof uses this declaration.