Example of antilogarithm with its equation
The concept of antilogarithm is used in the field of mathematics . This is what the number that has another given number is called as a logarithm .
General definition
It can be said that the antilogarithm of a number P in a certain base is that figure that, in the base in question , has P as a logarithm . As you can see, to understand what an antilogarithm is, it is essential to know what the idea of a logarithm refers to.
The exponent to which a positive number (the base ) must be raised to obtain a certain figure is called a logarithm . The exponent , for its part, is the number that indicates the power to which another figure must be raised.
The antilogarithm or antilog of a number to a certain base is the quantity that, in that base, has the number mentioned as a logarithm or log . It is important to consider that each negative or positive number corresponds to a logarithm of another number , which is its antilogarithm.
Practical example
We can state, for example , that the logarithm of 625 in base 5 is 4 . This is because 625 is equal to 5 to the power of 4 (i.e., to the 4th power ): 5 x 5 x 5 x 5 = 625 .
In short, the antilogarithm of P , in a given base, is the number that, in that base, has P as a logarithm. If, to base 5 , the logarithm of 625 is 4 , it is understood that 625 is the antilogarithm of 4 to base 5 .
Expressed another way : the antilogarithm of 4 in base 5 is the number that, in that same base (that is, in base 5 ), has 4 as a logarithm ( 625 , as we already saw).
Origin and applications
Since the concept of antilogarithm depends closely on that of logarithm for its definition, it is necessary to talk about the latter to understand it better. First of all, we should mention the usefulness of the logarithm, or one of them, since it is one of those difficult topics that in school are usually presented in an imposed way and without further explanations .
The main use of the logarithm has always been the simplification of operations such as division, multiplication and extraction of radicals, when dealing with numbers that are too large. It was very convenient to have tables of logarithms and antilogarithms to face these challenges. Needless to say, since the widespread use of scientific calculators, computers and mobile devices, their impact has been decreasing.
Regarding its origin, the first person to make an official presentation of the logarithm was John Napier , a Scottish scientist, in 1614, through his work entitled Description of a wonderful table of Logarithms . His surname is very important, since the name "Neperiano" is derived from it, another way of calling the natural logarithm.
The usefulness of the antilogarithm was losing strength with technological advances
An exponential function
Entering even more technical terrain, we can affirm that the antilogarithm is an exponential function , that is, one of type f(x) = ab x in which x is understood as an exponent. In fact, the function f(x) = ab px+q , for example, is also considered exponential because it can be rewritten as follows: (ab q )(b p ) x .
By having a real variable, these types of functions have the characteristic that their growth rate (a concept that in technical terms is known as the derivative ) has a direct proportion to the value of the function itself. Since by changing the base we obtain an additional constant factor, to reduce the computing cost it is recommended to study these functions to focus only on the analysis of the so-called natural exponential function , that is, the one in which everything is reduced to an expression raised to x .