...observations being understood, the following rule must be borne in mind. Rule. The index of the logarithm of a number greater than unity, is one less than the number of digits in the integral part, and when the number is less than unity, consisting of decimals only, then add...

...fraction. The integral part is called the charac teristic. and may be known from the following RULE. The characteristic of the logarithm of any number greater than unity, is one less than the number of integral figures in the given number. Thus the logarithm of 297 is 2 plus a fraction; that is, the...

...itself; hence only the mantissa is commonly given in the table5 Prop — The characteristic of the common logarithm of any number greater than unity, is one less than the number of integral figures in the given number' ILL- The logarithm of 4685 is more than 8, because 10' = 1000,...

...hence only the mantissa is commonly given in the table. 3. Prop. — The characteristic of the common logarithm of any number greater than unity, is one less than the number of integral figures in the given number. Ьл. The logarithm of 4685 is more than 3, because 10' = 1000,...

...hence only the mantissa is commonly given in the table. 5. Prop. — The characteristic of the common logarithm of any number greater than unity, is one less than the number of integral figures in the given number. ILL. The logarithm of 4685 is more than 3, because 10' = 1000,...

...hence only the mantissa is commonly given in the table. 5. Prop. — The characteristic of the common logarithm of any number greater than unity, is one less than the number of integral figures in the given number. ILL. The logarithm of 4685 is more than 8, because 10' = 1000,...

...of which is 3, and the mantissa -2375439. 1°. In the common system, the characteristic of the log of any number greater than unity is one less than the number of figures to the left of the decimal point. DEM. — If there be n + 1 figures to the left of the decimal...

...logarithm can always be obtained by the following rule : BULK. — The characteristic of the logarithm of a number greater than unity is one less than the number of digits in the whole number. The characteristic of the logarithm of a number less than unity is negative, and...

...number is therefore between n and n — 1 ; thus the logarithm is equal to n — 1 + a decimal. Thus the characteristic of the logarithm of any number greater than unity is one less than the number of figures in its integral part. Next, let the number be less than 1. Express the number as a decimal,...

...table, from which the following rules are immediately deduced. The characteristic of the logarithm of a number greater than unity is one less than the number of digits to the left of its decimal point. Thus the characteristic of the logarithm of 471 is 2, since 471 is...