What Does logarithm Mean
The etymology of logarithm leads us to two Greek words: lógos (which is translated as "reason" ) and arithmos (which can be translated as "number" ). The concept is used in the field of mathematics.
A logarithm is the exponent to which a positive quantity needs to be raised to obtain a certain number. It should be remembered that an exponent, meanwhile, is the number that denotes the power to which another figure must be raised.
Thus, the logarithm of a number is the exponent to which the base has to rise to arrive at that number . Many times an arithmetic calculation can be done more simply by appealing to logarithms.
Let's look at an example . The base 5 logarithm of 625 is 4 , since 625 is equal to 5 to the power 4 : 5 x 5 x 5 x 5 = 625 .
Given a number (the argument ), the logarithm function is in charge of assigning an exponent (the power ) to which another fixed number (the base ) must be raised to obtain the argument. Returning to our example, the argument is 625 , the power is 4, and the base is 5 .
Base on power = Argument
5 raised to 4 = 625
5 x 5 x 5 x 5 = 625
Scotsman John Napier is noted as the pioneer in defining logarithms in the seventeenth century . Years later, the Swiss Leonhard Euler linked them with the exponential function. In order to facilitate operations, engineers and scientists from different fields use logarithms on a daily basis.
It is called a logarithmic scale , on the other hand, to the measurement scale that uses the logarithm of a physical quantity in replacement of the quantity in question.
The concept of "measurement scale" is also known as "measurement level" and it is a variable that serves to describe the nature of the data that contains the numbers that are assigned to objects and, therefore, those that it contains a variable .
With respect to "physical quantity", it means one that can be measured in the context of a physical system , that is, to which it is possible to assign different values that start from a measurement.
Although the name may seem unusual, we have all used the logarithmic scale in school even without knowing it. For example, it can be seen in the divisions of the Cartesian axes that are separated by equal distances such as: 1, 10, 100, 1000, instead of 1, 2, 3, etc. This can be ideal for graphing data that spans a large range of values, as the range becomes much easier to manipulate.
The bases of logarithms that are most used are the number e , base of natural or natural logarithms, and 10 , that of decimals.
Thanks to the scientific studies of people like Ernst Heinrich Weber and Gustav Theodor Fechner , in the late 18th and early 19th centuries, respectively, we know that there is a quantitative relationship between the way we perceive physical stimuli and their magnitude . This theory was proposed in the year 1860 and, in other words, it can be expressed as that certain senses of the human being work in a logarithmic way .
This can help us understand some of the advantages of using logarithmic scales when representing certain values, since our brain understands the concept of logarithm in a much more natural way than we think. The ear, for example, is able to perceive equal differences in the height of sounds when stimulated by equal ratios of frequencies.
As if this were not enough, some studies carried out in groups of young children and adults from tribes far from the big cities have shown that human beings make use of logarithmic scales in a natural way to represent numerical values .