Is there any $\alpha$ for which $e^{\alpha}$ is an integer?

Question

Is there any $\alpha$ which gives $e^{\alpha}$ an integer.

$\alpha=0$ is the trivial one.

But is there any other than $0$?

Answer 1

Very common example is the value a=ipi

Answer 2

Yes, $\ln(n)$ where $n$ is any positive integer. You see $\ln$ is the natural logarithm and is the inverse of $\exp$.

Answer 3

Yes, of course. Any number of the form $\ln(n)$ with $n$ whole.

$e^x$ is a continuous map from $(-\infty,\infty)$ to $(0,\infty)$ so it is immediately necessary that for any integer you choose, there is some $x$ where $e^x$=it.