let a, b be Real; :: thesis: ( a > 0 & a <> 1 & b > 0 implies - (log a,b) = log a,(1 / b) )
assume that
A1: a > 0 and
A2: a <> 1 and
A3: b > 0 ; :: thesis: - (log a,b) = log a,(1 / b)
thus - (log a,b) = 0 - (log a,b)
.= (log a,1) - (log a,b) by A1, A2, POWER:59
.= log a,(1 / b) by A1, A2, A3, POWER:62 ; :: thesis: verum