Logarithms-Properties of Logarithms

This article is going to be focused on “logarithm” and “properties of logarithms”. “Logarithm” refers to the way of expressing the exponents and there are two types of “logarithm”. “Logarithm” is widely used to measure a specific that something has already been taken.

Definition and the mathematical concept of the “logarithm”

“Logarithm” refers to such a quantity that is used to represent the power that must be raised by a fixed number for producing the given number. Along with this, power or the component is also referred to by “logarithm” to which the power of the base needs to be raised for yielding the provided number. In this article, an example has been provided for a better understanding. If someone wants to find out what the “base ten logarithms” of 100 is, then it must be 2. Since then, ten have been raised to the power of two hundred. Therefore, it can be said that “log 100 = 2”.

It is believed that for expressing large numbers the most convenient way is “logarithm”. There are several important properties of a “logarithm” and these properties prove division and multiplication of “logarithms” may also be expressed in such a form of logarithm” of subtraction and addition.

On the other hand, it can be also said that other ways of writing components are also referred to by the term “logarithm”. A “logarithm” of a number with its base is considered equal to another number. Exponentiation is considered as the opposite function of a  “logarithm”. “102 = 100” can be taken as an example of a “logarithm”. 

Here it can be stated that “an = x” or “Logax = n” where a is denoting the base of the function of the “logarithm”. In this context, it can be also read as “base a is exactly equal to n x logarithm”. 

History of “logarithm”

The concept of “logarithm” has been introduced by John Napier in the seventeenth century. After the discovery, several scientists have used the concept of “logarithm” and along with scientists this concept has been used by several engineers and navigators as well. The concept of “logarithm” has been mainly used for calculating which made the process of calculator easy at that time. In a simple way, it can be stated that it was just an inverse process of exponentiation. That is hoe concept of “logarithm” has been discovered and people started using it for making the process of calculation easy than before.

Different types of “logarithm”

Most of the time, two types of “logarithm” are used, such as “natural logarithm” and “common logarithm”. The “natural logarithm” is considered as the base of “e” “logarithm”. The “natural logarithm” can be also expressed as loge or In. The Euler’s constant is represented by “e” and the value of “e” is equal to the value of 2.718528. The base of 10 logarithms is known as the “common logarithm”. “Common logarithm” can be expressed as simply log or log 10. This article is going to give a proper example of a “common logarithm”. Log (1000) can be taken as the common logarithm of 1000. 

Properties of logarithms

In this portion of this article few “properties of logarithms” have been provided such as:

Product property

Product property is one of the important “properties of logarithms”. If b, e and f are positive and b is not equal to the value of one then, logb(ef) = logbe +logbf. Therefore, it can be said that the log of two numbers e and f with their base “b” is exactly equal to the sum of the log e and log f with their same base “b”.

Quotient property

If e, f and b are conside4red as positive integers and the value of “b” is not equal to the value of one then: logb(e/f) = logbe – logbf

Here, in this expression, the logarithm of a quotient of these two positive numbers e and f result in a difference of log e and log f with their same base “b”.

Power rule

Power rule is also considered as the important “property of logarithms”. If b and e are considered as positive integers, the value of b is not equal to the value of one and f is considered as a real number, then:

Logbef = f logbe

Here, the power of “f” and logarithm power of a positive number is equal to the product value of “f” and the log value of “e”.

Conclusion

Usage of “logarithm” has started in the seventeenth century and from that time it has been used for making the calculation process to be easy. There are two types of “logarithm” which are mostly dealt with such as natural logarithm and common logarithm. There are several “properties of logarithms” as mentioned in the previous discussion of this article. Therefore, “logarithm” has great importance in the field of mathematics.