Theorem reglogbas

Description: General log of the base is 1. (Contributed by Stefan O'Rear, 19-Sep-2014) (New usage is discouraged.) Use logbid1 instead.

	Ref	Expression
Assertion	reglogbas	|- ( ( C e. RR+ /\ C =/= 1 ) -> ( ( log ` C ) / ( log ` C ) ) = 1 )

Proof

Step	Hyp	Ref	Expression
1		relogcl	|- ( C e. RR+ -> ( log ` C ) e. RR )
2	1	recnd	|- ( C e. RR+ -> ( log ` C ) e. CC )
3	2	adantr	|- ( ( C e. RR+ /\ C =/= 1 ) -> ( log ` C ) e. CC )
4		logne0	|- ( ( C e. RR+ /\ C =/= 1 ) -> ( log ` C ) =/= 0 )
5	3 4	dividd	|- ( ( C e. RR+ /\ C =/= 1 ) -> ( ( log ` C ) / ( log ` C ) ) = 1 )