Question

What is `ln(e^x)`?

Answer 1

It is exactly `x`.

Explanation:

You are looking for a number that is the exponent of the base of `ln` which gives us the integrand, `e^x`;
so:
the base of `ln` is `e`;
the number you need to be the exponent of this base to get `e^x` is.....exactly `x`!!!
so:
`ln(e^x)=log_e(e^x)=x`