Remember, logarithms are really, really complicated. This is literally my least favorite thing in math. As such, this wil probably be a very basic and completely unhelpful while still having a somewhat correct answer.
A natural logarithm is just in base10. Since it is in base10, all numbers that are 10^whatever are whole numbers when the logarithm is taken of it. As such, numbers such as 10, 100, 1000, and really long numbers like 1000000000000000000000000000000000000000000 are all able to have the natural logarithm taken of them.
Thus, the below equation is what I'm guessing you were trying to portray, correct?
$${log}_{10}\left({\sqrt{{\mathtt{100}}}}\right) = {\mathtt{1}}$$
This works because the square root of 100 is 10, and since 10 is a dual factor of, well, 10, the natural logarithm can be taken of it and the answer is one.
It would help if somebody who understood this better could give a more in-depth and sensible answer.
+1006 
