## Is lnn\ln n transcendental for all rational n>1n>1?

I know that lnn is transcendental for all integer n>1. But does this still hold for non-integer rational values of n>1? For example, is ln1.5 transcendental? EDIT: Somehow managed to overlook the fact that cases like lne=1 are not transcendental 😛 The question has been revised to only include rational numbers n. Answer No, what … Read more