Metamath Proof Explorer


Theorem reglog1

Description: General log of 1 is 0. (Contributed by Stefan O'Rear, 19-Sep-2014) (New usage is discouraged.) Use logb1 instead.

Ref Expression
Assertion reglog1 C + C 1 log 1 log C = 0

Proof

Step Hyp Ref Expression
1 log1 log 1 = 0
2 1 oveq1i log 1 log C = 0 log C
3 relogcl C + log C
4 3 recnd C + log C
5 4 adantr C + C 1 log C
6 logne0 C + C 1 log C 0
7 5 6 div0d C + C 1 0 log C = 0
8 2 7 syl5eq C + C 1 log 1 log C = 0