Question

What does \[Ln\] stand for?

Answer 1

Hint: 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.