Use the logarithm tables to find the logarithm of the following numbers 25975 (ii) 25.795

Explanation

(i) The characteristic of the logarithm of 25795 is 4.
To find the mantissa of the logarithm of 25795, we take the first four digits.
The number formed by the first four digits is 2579. Now, we look in the row starting with 25. In this row, look at the number in the column headed by 7. The number is 4099. Now, move to the column of mean differences and look under the column headed by 9 in the row corresponding to `2.5` . We see that the number there is `1.5`.
Add this number to 4099. We get the number 4114. This is the required mantissa. Hence,
` log(25795) = 4.4114`
(ii) The characteristic of the logarithm of `25.795` is 1, because there are two digits to the left of the decimal point. The mantissa is the same as in the above question. Hence,
` log 25.795 = 1.4114`.
Similarly , ` log 2.5795 = 0.4114.`
and ` log(0.25795) =- 1+ 0.4114 = bar(1).4114`
is a negative number of magnitude ` 1.4114," whereas " -1 + 0.4114 ` is equal to - 05886. In order to avoid this confusion, we write bar(1) for - 1, thus,
` log(0.25795) = bar(1).4114`.