If I have two integers $a,b > 1$. Is $\ln(a) - \ln(b)$ always either irrational or $0$. I know both $\ln(a)$ and $\ln(b)$ are irrational.
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 ...
Could someone provide, please, a proof of the theorem below? "Being x and b integers greater than 1, which can not be represented as powers of the same basis(positive integer) and integer exponent, ...