Theorems · Definition · number theory
Nat.log
ℕ → ℕ → ℕ
log b n, is the logarithm of natural number n in base b. It returns the largest k : ℕ
such that b^k ≤ n, so if b^k = n, it returns exactly k.
- Defined in
- Mathlib.Data.Nat.Log
- Cited by
- 101 results in Mathlib
- Foundations
- Depth 22 from the axioms, rests on 126 definitions · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Nat.log.goproof · cited by 7
Cited by103
Results whose statement or proof uses this declaration.
- Int.logproof · cited by 25
- Int.clogproof · cited by 21
- Nat.log_zero_rightstatement · cited by 18
- Nat.log_of_left_le_onestatement · cited by 12
- Nat.pow_log_le_selfstatement · cited by 9
- Int.log_of_right_le_oneproof · cited by 8
- Nat.le_log_of_pow_lestatement · cited by 8
- Int.log_of_one_le_rightstatement · cited by 8
- Nat.log_one_leftstatement · cited by 7
- Nat.log_mono_rightstatement · cited by 6
- Nat.log_zero_leftstatement · cited by 6
- Nat.le_log_iff_pow_lestatement · cited by 5