I have a hard time understanding why $\ln e=1$ I have a hard time understanding why $\ln e=1$

Can someone explain to me why the natural logarithm of e is exactly equal to the first nonzero but positive integer?
It depends on how you define the natural logarithm; but, let's do it this way:

By definition, $\ln(x)$ is the unique number $y$ such that $e^y=x$.  In other words, the natural logarithm $g(x)=\ln(x)$ is the inverse function for the exponential function $f(x)=e^x$.

So, $\ln(e)=1$ because $e^1=e$.
A logarithm (being a function) along with a base $b$, when given an input $x$, could be interpreted as "What is $y$ such that $x=b^y$".
So if $b=e$, when evaluating $\log_e(e)=\ln(e)$, we actually ask "What is $y$ such that $e=e^y$". Therefore $\ln(e)=y=1$ must hold..