In mathematics, the concept of logarithm refers to another way of expressing exponents. It can be called an inverse operation of exponential solutions. The logarithm of a number is calculated with a base value. The number on which the logarithm is done is the number that is the exponent of a fixed number and that fixed number is taken as the base of the logarithm.

In other words, if a number ‘a’ is raised to the power of ‘n’ to give a value of ‘b’, then it can be said that the logarithm (or log) of ‘b’ to the base ‘a’ gives the value ‘n’.

For example, 4 raised to the power of 3 gives the value 64. Therefore, log 64 to the base 4 is equal to 3.

Any exponential equation can be converted to a logarithm function and vice versa. A logarithm is a useful tool in solving various mathematical problems where only exponents do not serve the purpose.

Properties of Logarithm

There are certain properties or rules related to logarithms that help to identify, simplify, expand, or compress a group of logarithms. These are mentioned as follows:

• The logarithm with base e is called the natural logarithm.
• The logarithm with the base is denoted without any base and called the common logarithm.
• The logarithm of the product of two numbers is equal to the sum of logarithms of individual numbers, provided the base is the same for both numbers.
• The logarithm of the division of two numbers is equal to the difference of logarithms of individual numbers when the base of both numbers is the same.
• The logarithm of 0 is not defined because any number raised to the power of another number can never give the value of zero as output.
• The logarithm of 1 for any base is zero.
• The logarithm of any number having the same base gives a value of 1.

Log Table 

The logarithm of a number with a given base is the number of times the base is multiplied to get that number. Thus, logarithm indicates repeated multiplication. There is a chart that acts as a reference for finding the log value of any given number. This chart is called the log table. This is a very useful table that provides the simplest way of finding the value of the logarithm of a given number. There is no need to go for complex calculations but to use the log table to get the log value of a number in a much simpler way. The most common log table consists of the list of log values with the base 10.

 Process of Using the Log Table

There are certain rules and steps to be followed for reading a log table. These are explained as follows.

1. In the log table, check the row that corresponds to the first two digits of the number and take the column that indicates the third digit. Take the value of where these rows and columns intersect.
2. In the log table, for the same row, check the mean difference value corresponding to the column that indicates the value of the fourth digit of the number. 
3. The values obtained in step-2 and step-3 are added and the value of the sum thus obtained is called the mantissa part that denotes the decimal part of the log value of the given number. 
4. Check the number of digits to the left side of the decimal part of the given number. One less than this number of digits gives the characteristic part which denotes the integer part of the log value of the given number. 
5. Combining the characteristic part and mantissa part the log value of the given number is obtained.