362 ALGEBRA.
USE OF THE TABLE.
443. On pages 360-361 we give a four-place table containing the mantissæ of the common logarithms of all integers from 100 to 1000.
444. To find the logarithm of a number.
(a) Suppose the number consists of three figures, as 56.7.
In the column headed W find the first two significant figures. On a line with these and in the column having at the top the third figure will be found the mantissa. Thus on a line with 56 and in the column headed 7 we find 7536. To this, which is the decimal part of the logarithm, prefix the characteristic [Art. 436], and we have
log 56.7 = 1.7536.
(6) Since in common logarithms the mantissa remains unchanged when the number is multiplied by an integral power of 10, we change one or two-figure numbers into three-figure numbers by addition of ciphers before looking for the mantissæ . The mantissa of log 56 will be that of 560, the only change in the logarithm being in the characteristic.
Thus log 560 = 2.7482, log 56 = 1.7482.
In the same manner log 7 has for mantissa that of log 700.
log 700 = 2.8451, log 7 = 0.8451.
(c) Suppose the logarithm of a number of more than three figures, as 62543, is required. Since the number lies between 62500 and 62600, its logarithm lies between their logarithms. In the column headed N we find the first two figures, 62; On a line with these and in the columns headed 5, and 6, we find the mantissze .7959 and .7966. Prefixing the characteristic [Art. 436], we have
log 62600 = 4.7966, log 62500 = 4.7959.
