 Hello and welcome to the session. In this session we will discuss about logarithm. The logarithm of any number to a given base is the exponent the base should be raised to get the given number. So like if we have log of the number n to the base a is equal to x this means n of x is equal to n. For example log 100 to the base of 10 is equal to 2. This would mean that 10 which is the base to the power of 2 is equal to 100. The logarithm of 1 is equal to 0 then the logarithm of any number say a to the same base say a would be 1. Now if the base of the logarithm is not indicated it is taken as 10. The logarithms calculated logarithms. Now we discuss the components of logarithms. We have 2 components of logarithms which are the characteristic of the logarithm and the mantisa of the logarithm. Now the integral part of the logarithm is the characteristic of the logarithm. The decimal part logarithm is called the mantisa of the logarithm. First we discuss the characteristic of the logarithm which is the integral part of the logarithm. One logarithm which is calculated to the base 10 this shows the position of the decimal point in the associated number. So this means if the characteristic is known then the position of the decimal is also known. Now let's discuss the rules for determining the characteristic of a logarithm. For this if we have that the number whose characteristic is to be determined is greater than 1. Now in this case the characteristic of the number would be positive. It would be equal to the number of digits to the left of the decimal point or find out the characteristic logarithm of the number given as 27.003. As this number is greater than 1 so the characteristic would be equal to the number of digits to the left of the decimal point which would be 2 that is 1. So its characteristic is given as 1. The number to be less than 1 now in this case the characteristic would be negative would be equal to minus of the number of zeros the decimal point number the characteristic logarithm of the number 0.003. As this number is less than 1 so its characteristic would also be negative this would be equal to minus of the number of zeros between the decimal point and the first non-zero digit of the number. So as you can see there are two zeros between them so 2 plus 1 which is minus 3. So characteristic of logarithm of 0.003 is equal to minus 3. Next is the mantisa of a logarithm which is the the fractional part of the mantisa of a logarithm for the particular sequence, the position, the decimal. If we have log 11 is equal to 1.0414 as we given the log of this number so we can easily find out the characteristic and mantisa of this logarithm as we know that characteristic of a logarithm is the integral part so it would be 1. The mantisa is the decimal part so it would be 0.0414. In this session we have understood the concept of logarithms and in comparison of logarithms.