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Logarithm and the Logarithm Table

A table that is used to find the value of different logarithm functions is known as logarithm table. It is commonly referred to as a log table. The logarithm of any given number has two distinguished parts. The integral part is also known as the whole part is called characteristic while the decimal part is called the mantissa. While the characteristic can be known by simple inspection, the mantissa has to be obtained with the help of logarithm tables. In this article, we will discuss logarithm, logarithm tables, different uses of logarithms, and a lot more.

Logarithm

Logarithms are very much related to powers and exponents. In mathematical terms, the logarithm of a number is the index or the power to which the base must be raised to form the number, that is, to make it equivalent to the given number. If ‘a’ raise to x is equal to n, where n>0, a>0, and a is not equal 1, then, x is said to be the logarithm of the number n to the base ‘a’. Let us see some examples to understand it more clearly. 

  • 8 to the power 2 is equal to 64. Now, the logarithm of 64 to the base 8 is 2.
  • 2 to the power 6 is equal to 64. Now, the logarithm of 64 to the base 2 is 6.
  • 6 to the power 3 is equal to 216. Now, the logarithm of 216 to the base 6 is 3.

Fundamental Properties of Logarithm

  • The logarithm of the multiplication of the two numbers is equivalent to the addition of the logarithms of the numbers to the common base that is:

           logaxy = logax + logay

  • The logarithm of the division of two numbers is equivalent to the difference of their logarithms to the common base that is:

           logax/y = logax – logay

  • The logarithm of the number raised to the power is equivalent to the index of the power multiplied by the logarithm of the number to the common base that is:

           logax raise to n = n logam

Different Types of Logarithm

  • Binary Logarithm: It is a type of logarithm that uses two as the base. This type of logarithm is used extensively in the field of computer science.
  • Natural Logarithm: It is a type of logarithm that uses ‘e’ as the base. Here, e denotes the value, 2.71828. The use of natural logarithm is widespread in subjects like Physics and Mathematics because of their simpler derivative.
  • Common Logarithm: It is a type of logarithm that uses 10 as the base. The use of common logarithm is widespread in fields of engineering and science.

Uses of Logarithms in Real Life

Logarithms have immense application in the field of calculations of exponential equations. Equations that can take enormous amounts of time and hard work can be easily solved using logarithms. Talking about the practical aspects, it is used in the measurement of decibels, Richter scale, the brightness of the stars, and a lot more. Many experiments conducted in chemistry classes take the help of logarithms as in the case of measurement of acidity and alkalinity.

History of Logarithm and Logarithm Table

The discovery of logarithms was done by the Scottish mathematician, John Napier in 1914. The sole purpose for which he discovered logarithms was to assist in the multiplication of quantities called sines. In 1620, the first logarithm table was created and published in Prague by the Swiss mathematician, Joost Burgi. If you want to learn more about logarithms and the logarithms table, or about the history of origination of these wonderful concepts in a fun and interesting manner, visit Cuemath.

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