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Mirrors > Home > MPE Home > Th. List > df-logb | Structured version Visualization version Unicode version |
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". The definition is according to Wikipedia "Complex logarithm": https://en.wikipedia.org/wiki/Complex_logarithm#Logarithms_to_other_bases (10-Jun-2020). (Contributed by David A. Wheeler, 21-Jan-2017.) |
Ref | Expression |
---|---|
df-logb | logb |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | clogb 24502 | . 2 logb | |
2 | vx | . . 3 | |
3 | vy | . . 3 | |
4 | cc 9934 | . . . 4 | |
5 | cc0 9936 | . . . . 5 | |
6 | c1 9937 | . . . . 5 | |
7 | 5, 6 | cpr 4179 | . . . 4 |
8 | 4, 7 | cdif 3571 | . . 3 |
9 | 5 | csn 4177 | . . . 4 |
10 | 4, 9 | cdif 3571 | . . 3 |
11 | 3 | cv 1482 | . . . . 5 |
12 | clog 24301 | . . . . 5 | |
13 | 11, 12 | cfv 5888 | . . . 4 |
14 | 2 | cv 1482 | . . . . 5 |
15 | 14, 12 | cfv 5888 | . . . 4 |
16 | cdiv 10684 | . . . 4 | |
17 | 13, 15, 16 | co 6650 | . . 3 |
18 | 2, 3, 8, 10, 17 | cmpt2 6652 | . 2 |
19 | 1, 18 | wceq 1483 | 1 logb |
Colors of variables: wff setvar class |
This definition is referenced by: logbval 24504 logbmpt 24526 logbfval 24528 |
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