An excerpt from the book: EXPLANATION OF THE TABLES. COMMON LOGARITHMS. FORM OF A LOGARITHM. The Logarithm of a number is the exponent of that power to which another number, the base, must be raised to give the number first named. The base commonly used in computation is 10, and as most numbers are incommensurable powers of 10, a common logarithm, in general, consists of an integer, the characteristic, and an endless decimal, the mantissa. If a number be resolved into two factors, of which one is an integer power ...
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An excerpt from the book: EXPLANATION OF THE TABLES. COMMON LOGARITHMS. FORM OF A LOGARITHM. The Logarithm of a number is the exponent of that power to which another number, the base, must be raised to give the number first named. The base commonly used in computation is 10, and as most numbers are incommensurable powers of 10, a common logarithm, in general, consists of an integer, the characteristic, and an endless decimal, the mantissa. If a number be resolved into two factors, of which one is an integer power of 10 and the other lies between 1 and 10, then the integer exponent of 10 is the characteristic, and the logarithm of the other factor is the mantissa. The characteristic is positive if the number be larger than unity, and negative if it be smaller; the mantissa is always positive. A negative characteristic is indicated by the sign - above it. E.g., 7770 = 103 x 7.77, and log 7770 = 3.890421, .0777 = 10-2 x 7.77, and log .0777 = 2.890421. The logarithms of all numbers expressed by the same figures in the same order have different characteristics but the same mantissa; for since all such numbers may be got one from another by multiplying or dividing by some integer power of 10, their logarithms differ by integers. In particular: if the decimal point stand after the first figure of a number, counting from the left, the characteristic is 0; if after two figures, it is 1; if after three figures, it is 2, and so on. So, if the decimal point stand before the first significant figure, the characteristic is 1; if one zero follow the decimal point, it is 2. E.g., log 3649 = 3.562174, log 3.649 = 0.562174, log .003649 = 3.562174. ...
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