Logarithms-Logarithms

John Napier was one who first evolved concept of “logarithm” during 17th century. Later on, it was used by numerous scientists, engineers, navigators and many more in the performance of numerous calculations that made it easier. In easier words, “logarithm” is said to be the reverse procedure of exponentiation.

Concept of Logarithm

“Logarithm” is nothing; rather it is an alternative way of expressing the exponents. Rather, it is used in solving problems that cannot be solved by using exponents only.  “Logarithm” is said to be the most appropriate way of expressing bigger numbers. A “logarithm” can have numerous essential and vital properties which help in proving the multiply and dividing of “logarithm”. These can be also generally written in the form of summation and subtraction.

It can be stated that the “logarithm” of any real number that is positive suppose x, in regard base y is generally the value of 1. From the following, it can be said that:-

• x and y are two real numbers that are said to be positive.
• y acts as a real number
• x is said to be an argument that is within the  “logarithm”
• y basically refers to the base of the “logarithm table” that is situated mainly at the bottom point of the  “logarithm”.

Types of Logarithm

Basically, while speaking about the nature of   “logarithm”, it can be stated that mainly there are two types of “logarithm” namely:

• Common Logarithm: It is generally known by the name of the decimal logarithm. Common Logarithm is generally symbolized by log 10. It is generally opined that a common logarithm is supposed to have a base number of 10. This base number 10 is constant in nature and it does not change at all. This type of “logarithm” is generally applied in calculus and other scientific calculations.

• Natural Logarithm: – Natural logarithm implies the baseline of a particular number and is eventually said to be a reverse function for a function of exponents. Generally, it can be said that natural logarithms are exceptional categories for “logarithm”.  These are generally being used to solve the problems that are being related to time and growth.

To keep the “logarithm formula” in mind, it is very much essential to deeply understand the “logarithm table” otherwise the solution would turn in the wrong direction.

Logarithm Table and determination of log number by using log table

In mathematics, a “logarithm table” can be used in finding the different sort of values in the function of “logarithm”. The easier and simpler way, method and technique in finding the value of any given function of “logarithm” is generally determined by applying and using the “logarithm table”. To have well-depth knowledge about “logarithm table”, some of the essential “logarithm formula” is needed to be kept in mind.

Following is the process of finding the log value of any given number by using log “logarithm table” that is broadly discussed below:

Step No. 1: The first and foremost step is to generally understand the basic core and idea of “logarithm”. It is being found that per “logarithm table” can be appropriately used at a given particular baseline. A frequent type of “logarithm table” generally used as base number 10.

Step No. 2:  After having an in general idea “logarithm”, students are bound to guess and analyse the different salient characteristics and mantissa of any given specific number

Step No. 3: Thirdly, students have used an in general “logarithm table”. After that, they have to use and properly check the column.  They also have to write down corresponding values against them to determine   “logarithm formula”.

Step No. 4: Students are found to use the “logarithm table” and determine a mean difference

Step No. 6: After determination of the mean difference in the “logarithm table”, students are bound to determine and find characteristic parts by using the  “logarithm formula”.

Step No. 7: Last and foremost step is to undertake a combination of both the characteristics as well as mantissa part of the “logarithm table” by determining the “logarithm formula”.

Practical application of Logarithm 

It can be cited that “logarithm” is useful in solving equations related to exponents. Some instances can be cited like decibel in measuring sound, Richter scale in measurement of the earthquake and many more. All engineers are found using the two typologies of “logarithm” entitled natural, common “logarithm”. Chemical engineers are using a “logarithm table” in measurement of radioactive decaying, major pH solutions, which are measured on a “logarithm table”  by an intensive application of the “logarithm formula”.

Conclusion

From the above discussion, it can be concluded by saying that a “logarithm” is basically a numerical operation that examines and evaluates how many times does a particularly given number, which is called the base, is being multiplied by the same in reaching another number.  It can be cited that with the help of the “logarithm table”, by applying the “logarithm formula” logs are considered very much significant in computer science. “Logarithm” at its best describes the prevailing number of octaves which is presented in between notes.