Page:Elementary algebra (1896).djvu/380

362 ALGEBRA. USE OF THE TABLE.

443. On pages 360-361 we give a four-place table containing the mantiss 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 mantiss. 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.