Question

What is the natural log of zero?

Answer 1

Difficult one!

Explanation:

This is a tricky question because you do not have a unique answer...I mean, you do not have an answer such as: "the result is 3".
The problem here rests in the definition of log:
`log_ax=b -> x=a^b`
so basically with the log you are looking for a certain exponent that when you rise the base to it gives you the integrand.

Now, in your case you have:
`log_e0=ln0=b`
where `ln` is the way to indicate the natural log or log in base `e`.

But how do you find the right `b` value such that `e^b=0`????

Actually it doesn't work...you cannot find it...you cannot rise to the power of a number and get zero!
If you try with a positive `b` it doesn't work (it gets bigger and not zero); for `b=0` it is even worse because you get `e^0=1`!
One thing you can do is to manipulate it to get as near as possible to zero...
if you take a negative exponent you can get almost there:
if `b` is VERY big (negatively) you get very near to zero:

for example: `e^-100=1/e^100=3.72xx10^-44`!!!!

basically if `b->-oo` then `x=e^b->0`
So I would say that `ln0->-oo` using "tends to" instead of “equal to”.