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Definition df-logb 24420
 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 24419 . 2 logb
2 vx . . 3
3 vy . . 3
4 cc 9019 . . . 4
5 cc0 9021 . . . . 5
6 c1 9022 . . . . 5
75, 6cpr 3839 . . . 4
84, 7cdif 3303 . . 3
95csn 3838 . . . 4
104, 9cdif 3303 . . 3
113cv 1652 . . . . 5
12 clog 20483 . . . . 5
1311, 12cfv 5483 . . . 4
142cv 1652 . . . . 5
1514, 12cfv 5483 . . . 4
16 cdiv 9708 . . . 4
1713, 15, 16co 6110 . . 3
182, 3, 8, 10, 17cmpt2 6112 . 2
191, 18wceq 1653 1 logb
 Colors of variables: wff set class This definition is referenced by:  logbval  24421
 Copyright terms: Public domain W3C validator