364 ALGEBRA.
446. To find the number corresponding to a logarithm.
(a) Suppose a logarithm, as 1.7466, is given to find the corresponding number.
Look in the table for the mantissa .7466. It is found in the column headed 8 and on the line with 55 in the column headed N. Therefore we take the figures 558, and, as the characteristic is 1, point off two places, obtaining the number 55.8.
(b) Suppose a logarithm, as 3.7531, is given to find the corresponding number.
The exact mantissa, .7531, is not found in the table, therefore take out the next larger, .7536, and the next smaller, .7528, and retain the characteristic in arranging the work.
Thus, the number corresponding to 3.7536 is 5670 and the number corresponding to 3.7528 is 5660 differences .0008 10
Now the logarithm 3.7531 is .0003 greater than the logarithm 3.7528, and a difference in logarithms of .0008 corresponds to a difference in numbers of 10; therefore we should increase the number corresponding to the logarithm 3.7528 by .0003 .0008 or 3 8 of 10.
Thus the number corresponding to the logarithm
3.7531 = 5660 3.7 correction = 5663.7
(c) Suppose a logarithm, as 8.8225 - 10 or 2.8225, is given to find the corresponding number.
Take out the mantissæ as in the previous example.
The number corresponding to 2.8228 is .0665 [Art. 437.] The number corresponding to 2.8222 is .0664 differences .0006 .0001
Now the logarithm 2.8225 is .0003 greater than the logarithm 2.8222, and a difference in logarithms of .0006 corresponds to a difference in numbers of .0001; therefore we
