Editing Hilbert's seventh problem (section)

==Solution==
The question (in the second form) was answered in the affirmative by [[Aleksandr Gelfond]] in 1934, and refined by [[Theodor Schneider]] in 1935. This result is known as Gelfond's theorem or the [[Gelfond–Schneider theorem]]. (The restriction to irrational ''b'' is important, since it is easy to see that <math>a^b</math> is algebraic for algebraic ''a'' and rational ''b''.)

From the point of view of generalizations, this is the case

:<math>b \ln{\alpha} + \ln{\beta} = 0</math>

of the general linear form in logarithms, which was studied by Gelfond and then solved by [[Alan Baker (mathematician)|Alan Baker]]. It is called the Gelfond conjecture or [[Baker's theorem]]. Baker was awarded a [[Fields Medal]] in 1970 for this achievement.