Show that $\log_7 n$ is either an integer or an irrational number where n is a positive number.
I assumed that it is rational and tried to get a contradiction for $\log_7 n = a/b$, where b does not divide a, but how can I show that $7^{a/b}$ is not an integer to achieve a contradiction since n is an integer ? If I can exclude rational numbers from the range of log function then it is either integer or irrational.
Or do you suggest other methods ?