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Definition df-logb 27758
 Description: Define the logb operator. This is the logarithm generalized to an arbitrary base. It can be used as logb for "log base B of X". In the most common traditional notation, base B is a subscript of "log". You could also use logb, which looks like a less-common notation that some use where the base is a preceding superscript. Note: This definition doesn't prevent bases of 1 or 0; proofs may need to forbid them. (Contributed by David A. Wheeler, 21-Jan-2017.)
Assertion
Ref Expression
df-logb logb
Distinct variable group:   ,

Detailed syntax breakdown of Definition df-logb
StepHypRef Expression
1 clogb 27757 . 2 logb
2 vx . . 3
3 vy . . 3
4 cc 9491 . . . 4
5 cc0 9493 . . . . 5
6 c1 9494 . . . . 5
75, 6cpr 4029 . . . 4
84, 7cdif 3473 . . 3
95csn 4027 . . . 4
104, 9cdif 3473 . . 3
113cv 1378 . . . . 5
12 clog 22767 . . . . 5
1311, 12cfv 5588 . . . 4
142cv 1378 . . . . 5
1514, 12cfv 5588 . . . 4
16 cdiv 10207 . . . 4
1713, 15, 16co 6285 . . 3
182, 3, 8, 10, 17cmpt2 6287 . 2
191, 18wceq 1379 1 logb
 Colors of variables: wff setvar class This definition is referenced by:  logbval  27759
 Copyright terms: Public domain W3C validator