1 and 1 hence their logarithms lie between -1 and 0, i.e., 1 = -1 and log 1 = 0, hence the common logarithm of a number between. (ii) To find the characteristic of the logarithm of a number lying between 0 and 1:

Accordingly, we have the following rule: The characteristic of the logarithm of a number greater than 1 is positive and is one less than the number of digits in the integral part of the number. In general, the characteristic of the logarithm of a number whose integral part consists of n digits is n - 1. Similarly, the characteristic of the logarithm of a number whose integral part consists of 3 digits is 2. Therefore, the characteristic of each of log 36, log 86.2 or log 90.46 is 1. Log 90.46 = 1 + a positive decimal part = 1∙ …… Log 86.2 = 1 + a positive decimal part = 1∙ …… Log 36 = 1 + a positive decimal part = 1∙ …… Therefore, the characteristic of each of log 5, log 8.5 or log 9.64 is 0.Īgain, the common logarithm of a number whose integral part consists of two digits only (i.e., of a number between 10 and 100) lies between 1 and 2 (log 10 = 1 and log 100 = 2).įor example, the integral part of each of the numbers 36, 86.2, 90.46 consists of two digits hence their logarithms lie between 1 and 2, i.e., Log 9.64 = 0 + a positive decimal part = 0∙ …. Log 8.5 = 0 + a positive decimal part = 0∙ …. Log 5 = 0 + a positive decimal part = 0∙ ……

For example, each of the numbers 5, 8.5, 9.64 lies between 1 and 10 (see that the integral part of each of them consists of one digit only) hence their logarithms lie between 0 and 1 i.e., Since, log 1 = 0 and log 10 = 1, hence the common logarithm of a number between 1 and 10 (i.e., whose integral part consists of one digit only) lies between 0 and 1. (i) To find the characteristic of the logarithm of a number greater than 1: The characteristic of the logarithm of a number is determined by inspection and the mantissa by logarithmic table. Since log 3 = 0.4771 and log 10 = 1, so the characteristic of log 3 is 0 and the mantissa of log 10 is 0.ĭetermination of Characteristic and Mantissa: 9742, then - 3 is the characteristic and. Suppose, log 39.2 = 1.5933, then 1 is the characteristic and 5933 is the mantissa of the logarithm. The integral part of a common logarithm is called the characteristic and the non-negative decimal part is called the mantissa. One part is integral which may be zero or any integer (positive or negative) and the other part is non-negative decimal. 01 lies between - 3 and -2 and so on.įrom the above discussions it is observed that the common logarithm of a positive number consists of two parts. Similarly, the logarithm of a number between. Therefore, the logarithm of a number between.

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