What is the natural log of 0?

The natural log of 0, ln(0), is undefined in the real number system. This is because there is no real number x that satisfies the equation e^x = 0, where e is Euler's number approximately equal to 2.71828.

In the complex number system, ln(0) is also undefined because there is no unique complex number that can be exponentiated to equal 0. This is because exponential functions are periodic in the complex plane with infinitely many values for each value of x.

It is worth noting that the limit of ln(x) as x approaches 0 from the positive side is negative infinity, meaning that ln(x) becomes increasingly large and negative as x gets closer to 0.