Definition of
natural logarithm
Before fully entering the meaning of the term natural logarithm that concerns us now, we are going to proceed to discover the etymological origin of the two words that shape it:
-Logarithm, first of all, derives from the Greek. A good example of this is that the result of the sum of two lexical components of said language: “logos”, which means “word”, and “arithmós”, which can be translated as “relative number”. It is a term that was used for the first time by the Scottish-born mathematician John Napier (1550 – 1617). He was the pioneer, therefore, in defining logarithms.
-Natural, secondly, comes from Latin. Exactly emanates from “naturalis”, which means “related to nature” and which is formed from the union of these lexical components: the adjective “natum”, which is equivalent to “born”; the suffix “-ura”, which is used to indicate the result of the action, and the suffix “-al”, which means “relative to”.
It is called logarithm the number to which a positive quantity must be raised for the result to be a certain number. The logarithm function, therefore, assigns a exponent (a power) to a number (called argument), to which the base (another number) has to rise to get it.
This means that the base raised to the power should yield the argument. He base 3 logarithm of 81 is 4given that 81 (the argument) is equal to 3 (the base) raised to the power 4.
Base to power = Argument
3 to the power of 4 = 81
3 x 3 x 3 x 3 = 81
according to their characteristicsThere are different types of logarithms. He natural logarithmalso called natural logarithmis the one that has the number e as base.
As can be seen, to understand what a natural logarithm is, it is essential to understand the concept of number e. That’s what one is called mathematical constant Which is equivalent to 2.718281828459…
This number e is the base of the natural logarithms. It’s about a transcendental number (i.e., not algebraic) and irrational (your decimal expression is not periodic nor exactly).
It can therefore be said that the natural logarithm of a number x is the exponent to which the value must be raised number e to get as a result x. The mathematician Nikolaus Mercator (1620-1687) is noted as the first person to mention the idea of natural logarithm in a publication, although at first it was given the formal name of hyperbolic logarithm since their values were corresponding to those of the sector located below the hyperbola.
In addition to everything indicated, we have to state that the natural logarithm has different applications. However, among the most significant we can highlight the following:
-To calculate what radioactive decay is.
-It is widely used in the field of statistics to proceed to transform the data. A transformation that may be necessary for different reasons.
-To calculate the probability density functions.
-It can be used to work with what is the exponential growth in the so-called biological populations.