Question

What does $Ln$ stand for?

Answer 1

We are asked to explain what $Ln$ stand for. It is one of the logarithm functions. Different logarithmic functions have different bases. The base of a logarithm function determines what logarithm function it is. $Ln$ stands for natural logarithm. And it has the base of exponential, $e$.

Complete step-by-step solution:
According to the given question, we are given a function which we have to recollect or recognize.
$Ln$ is one of the logarithm functions and it has a base of exponential, $e$. There are different logarithm functions and each of those logarithm functions are differentiated through their bases. The base of a logarithm function determines the logarithm property of that particular logarithm function.
$Ln$, specifically, is the natural logarithm and has the base of exponential, $e$. The exponential, $e$ is an infinitely long number, that is, it is an irrational number. The value of e is $2.718281828...$.
The natural logarithm is usually used. It is also represented as $lo{{g}_{e}}$
Now, there is another logarithm function with base 10. The logarithm function with the base 10 and it is represented as $lo{{g}_{10}}$.
Similarly, other logarithm functions with different bases.
But, we usually use the natural logarithm for our requirements, as the coefficients on the natural-log can be interpreted easily and can be approximated as well.
The difference in computation of natural logarithm and $lo{{g}_{10}}$ is as follows,
$\ln (10)=2.302$
$lo{{g}_{10}}10=1$

Note: The logarithm function should be dealt with carefully and the base of the logarithm function is of importance.
Also, ${{b}^{x}}=n$ and the logarithm equivalent is,
$x={{\log }_{b}}n$
Irrespective of the base used in the logarithm function, the basic properties of a logarithm function remain the same.