Any real number is some power of $e$ (because $\ln(x)$ has values in the range $(-\infty , + \infty)$.
Say, $5$ is a rational number. So there is some $x$ which makes $\exp(x)= 5$.
What is $x$? rational , irrational?
A power of $e$ leads to $5$, Will it be an infinite series converging to the value $5$?
Can a combination of irrational number result into a rational number?