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Definition df-log_ 28515
Description: Define the log_ operator. This is the logarithm generalized to an arbitrary base. It can be used as  ( (log_ `  B ) `  X ) for "log base B of X". This formulation suggested by Mario Carneiro. (Contributed by David A. Wheeler, 14-Jul-2017.)
Assertion
Ref Expression
df-log_  |- log_  =  ( b  e.  ( CC 
\  { 0 ,  1 } )  |->  ( x  e.  ( CC 
\  { 0 } )  |->  ( ( log `  x )  /  ( log `  b ) ) ) )
Distinct variable group:    x, b

Detailed syntax breakdown of Definition df-log_
StepHypRef Expression
1 clog_ 28514 . 2  class log_
2 vb . . 3  set  b
3 cc 8751 . . . 4  class  CC
4 cc0 8753 . . . . 5  class  0
5 c1 8754 . . . . 5  class  1
64, 5cpr 3654 . . . 4  class  { 0 ,  1 }
73, 6cdif 3162 . . 3  class  ( CC 
\  { 0 ,  1 } )
8 vx . . . 4  set  x
94csn 3653 . . . . 5  class  { 0 }
103, 9cdif 3162 . . . 4  class  ( CC 
\  { 0 } )
118cv 1631 . . . . . 6  class  x
12 clog 19928 . . . . . 6  class  log
1311, 12cfv 5271 . . . . 5  class  ( log `  x )
142cv 1631 . . . . . 6  class  b
1514, 12cfv 5271 . . . . 5  class  ( log `  b )
16 cdiv 9439 . . . . 5  class  /
1713, 15, 16co 5874 . . . 4  class  ( ( log `  x )  /  ( log `  b
) )
188, 10, 17cmpt 4093 . . 3  class  ( x  e.  ( CC  \  { 0 } ) 
|->  ( ( log `  x
)  /  ( log `  b ) ) )
192, 7, 18cmpt 4093 . 2  class  ( b  e.  ( CC  \  { 0 ,  1 } )  |->  ( x  e.  ( CC  \  { 0 } ) 
|->  ( ( log `  x
)  /  ( log `  b ) ) ) )
201, 19wceq 1632 1  wff log_  =  ( b  e.  ( CC 
\  { 0 ,  1 } )  |->  ( x  e.  ( CC 
\  { 0 } )  |->  ( ( log `  x )  /  ( log `  b ) ) ) )
Colors of variables: wff set class
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