Question

What is `e^(ln(x)`?

Answer 1

It's `x`.

Explanation:

The logarithm and the exponential are inverse function, which means that if you combine them, you obtain the identity function, i.e. the function `I` such that `I(x)=x`.

In terms of definitions, it becomes obvious. The logarithm `ln(x)` is a function which tells you what exponent you must give to `e` to obtain `x`. So, `e^(log(x))`, literally means:

"`e` to a power such that `e` to that power gives `x`".