That is just an obvious extension of the rule that log(ab)=b×log(a). It is not worthy of any special term. I suppose the formula might be helpful in answering some questions about the probability of a succession of losses. For example, suppose a video poker player wants to know how many hands he would have to play, such that the probability of a royal drought is exactly 5%. The probability of a royal per hand in 9/6 Jacks or Better, with optimal strategy, is 0.00002476. The degree of certainty that at least one royal will appear is 95%. So, the number of hands in a 5% royal drought would be log(1-.95)/log(1-0.00002476) = 120,989.
However, you don’t need to use that formula to solve that problem. It could be set up as:
.05 = (1-0.00002476) n
n
log(.05) = n × log(1-.00002476)
-1.301 = n × -0.000010753
n = 120,989