For example, when X = –2, log(X) = log(-2) = 0, then X cannot be greater than -2. In other words, there is no number that can be greater than -2 unless it has a negative answer. 

Let’s say Y uses the base X and Y=0 if X > -2; Y=-2 if X < -3; Y=-1 if -3 < X < 0, etc. 

Then if we work out the value of Y for each value of X it turns out that we can plot a curve that will give us some information about how

The natural logarithm of a number has the unique property that when added to its value, it results in the additive inverse.

The natural logarithm of a negative number is called the Log of negative numbers and has a base equal to -1. 

The implicit function theorem states that if formula_1 are continuous functions on a closed interval formula_2 then:

Some people think that the log of a negative number cannot be computed. However, this is incorrect. 

Any function \(f(x) = x^p\) can be rewritten as \(f(x) = (1/e) \ln (1/X) + C\). If we let \(X=-n\), then \(C=n\) and this function is the inverse of a function with pole at 0. 

This shows that every value of \(x\) in \(-n \le x < n\) has a unique representation \(\log_{-n} (x)\) by elementary algebra.

How Negative Numbers work?

Have you ever wondered why when you have a number such as -2 it is negative? What actually makes it a negative number. It makes no logical sense why negative numbers should work any differently than positive numbers. 

Introduction: Negative numbers have been used for thousands of years. 

In 3500 BC, the Sumerians used negative numbers to represent debts. 

They probably had no idea what they were doing, but it ended up working out since they would eventually create the world's first known civilization.

History of Numbers

Most people will typically tell you that the history of numbers begins with the rise of humanity, and dates back to around 4000 BC

That is how far most civilizations could count, before their languages became too complex for them, and they decided to create numerals out of stone or clay. 

This visual representation of numbers as we know them today helped early humans keep track of who owns which animals and property. 

It is also from this time onward that we could date back to the first recorded history of numbers.

The history of numbers is a long and eventful story that has led humanity through the millennia to the stage we have reached today. 

It’s a journey that reveals how numbers have been used, the many different roles they have played and functions they have fulfilled, and how this knowledge has been acquired, codified and passed on. 

Last Words

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