............................ — 2-793830 Therefore the index or characteristic of any logarithm is always l less than the number of figures in the integral part of the natural number. Explanation and use of the TalJe of Logarithms. 170. THE table contains the logarithms...

...in part, decimal, the index must be changed accordingly. Observing that the index must always be one less, than the number of figures in the integral part of the given number; also, when the given number is wholly a decimal, the index is negative, and must be one...

...greater than 1 and less than 2, that is, they are 1 with some fraction annexed, and so on. The mhole numbers or integers in the logarithmic series are...generalize, let us assume the two following series : г-, г*, г*', т*', &c. . (1) у , у' , у", у'", &с. . (2) in which r is some given number...

...numbers or decimals, will be the same, with the exception of the characteristic, which will always be one less than the number of figures in the integral part of the number. For example; taking the number 654685, and dividing it successively by 10, and for each division...

...or thousands, the index is 3 ; and so on uniformly, as in the foregoing series, the index being one less than the number of figures in the integral part of the natural number. The decimal part of a logarithm is the same, whether the natural number to which it...

...2-60906, where 2 is the characteristic and -60906 is the mantissa. As the characteristic is always 1 less than the number of figures in the integral part of the number, the logarithm given in the tables is only the decimal part of the required logarithm, and the...

...must be changed in accordance with the principles laid down in Art. 7. Thus, the index must be one less than the number of figures in the integral part of the natural number. But when the natural number is wholly a decimal the index is negative, and must be...

...log 100 =2, 1000 = 10*, log 1000 = 3. Hence the characteristic for a number greater than unity is one less than the number of figures in the integral part of the number. it affects only the characteristic and not the mantissa, which always remains positive. Since...

...and 10"; so its logarithm lies between n — 1 and n. That is, the characteristic is n — 1, -or one less than the number of figures in the integral part of the given number. 2. When the number is less than unity, suppose it a decimal with n cyphers immediately...

...the following rule : RULE. The characteristic of the logarithm of a number greater than unity is one less than the number of figures in the integral part of the number. The characteristic of a number less than unity is negative, and (when the number is expressed...