Answer
The base for the natural logarithm is defined using the fact that the natural logarithmic function is continuous, is one-to-one, and has a range of $(-\infty, \infty)$
So, there must be a unique real number such that $ln(x) = 1$. This solution to this equation is denoted by the letter $e$.
Work Step by Step
We know that:
(i) $ln(1) = 0$
(ii)$\lim\limits_{n \to \infty}ln(n) = \infty$
(iii)The natural log function is continuous
By these three facts, there must be a number(let's call it $e$) for which the function assumes the value 1. It also follows from this that $e>1$.
Indeed $$e = 2.718.. >1$$
