It concerns the irrationality and transcendence of certain numbers (Irrationalität und Transzendenz bestimmter Zahlen).
Two specific equivalent[1] questions are asked: The question (in the second form) was answered in the affirmative by Aleksandr Gelfond in 1934, and refined by Theodor Schneider in 1935.
From the point of view of generalizations, this is the case of the general linear form in logarithms, which was studied by Gelfond and then solved by Alan Baker.
It is called the Gelfond conjecture or Baker's theorem.
Baker was awarded a Fields Medal in 1970 for this achievement.