log (1)

i. [LOG (1), s.] To cut and get out logs. log (2), v. t. [LOG (1), s.] To enter in a log-book. different values of z will be found in each system, and such numbers being registered will form tables of logarithms. The Common, or Briggs', tables of Logarithms are calculated to base 10. The Napier ian tables, invented by Lord Napier, are calculated to base e ( epsilon ), which=2.7182818. In the common system of logarithms, the logarithm of 100 is 2, because 10 raised to the second power=100; similarly, the logarithm of 1000=3, of 10000=4, and so on. When the logarithms form a series in arithmetical progre ion, the corresponding natural numbers form a series in geometrical progre ion, thus: Logarithms.. 1 10 102 1003 10000 100005 The logarithms of numbers between 1 and 10 con. sist of decimals; of numbers between 10 and 100 they consist of the integer 1 and a decimal; of numbers between 100 and 1000 of the integer 2 and a decimal, and so on. The integral part of a logarithm is called the index, and it is always le by 1 than the number of integer places in the corresponding natural number: thus the index of the logarithm of 3 is 0, of 30 is 1 of 300 is 2, and so on. The logarithms of decimals have negative indices, and the number of units in the index is always greater by 1 than the number of ciphers immediately following the dec i mal point: thus the index of the logarithm of 3 is -1, of '03 is-2, of 003 is -3 and so on. The decimal part of a logarithm is called the manti a. Logarithms are of great service in shortening and facilitating the arithmetical operations of multiplication and division; for since the sum of the logarithms of two numbers is the logarithm of the product of those numbers; and since logarithms are the indices of powers of the same basis, the difference of the logarithms of two numbers is the logarithm of the quotient; also the multiple of the logarithm of a number is the logarithm of the power of that number, and a fraction of the logarithm of a number is Natural numbers 1 10 100 1000 10000 100000 chin, bench; go, gem; thin, this; sin, as; expect, Xenophon, exist. ph = f. log arithmetic the logarithm of the corresponding root. Hence a complete table of logarithms would enable us to perform multiplication by addition, division by subtraction, involution by multiplication, and evolution by division. Logarithms were invented by Lord Napier of Merc hist on in Scotland in 1614, and improved by Henry Briggs, Savillian Profe or of Geometry at Oxford in 1624. (1) Arithmetical complement of a logarithm : The difference between the given logarithm and 10. (2) Hyperbolic logarithms : The Napierian system of logarithms, so called from their relation to certain areas included between the equilateral hyperbola and its asymptotes. "There is no reason why the Napierian logarithms should be called hyperbolic , rather than those of any other system; for, the same relation which exists between the Napierian system and the equilateral hyperbola also exists between other systems and oblique hyperbolas. In the case of oblique hyperbolas, the area is limited by two oblique ordinates, and the modulus of the system is always equal to the sine of the angle between the ordinates."- Davies & Peck : Mathematical Dict.: Logarithms. log-a-rith-met-ic, *log-a-rith-met-ic-al, a . [Formed on analogy of arithmetic, arithmetical .] Of or pertaining to logarithms; logarithmic. log-a-rith-met-ic-al-ly, adv. [Eng. logarith metical; -ly.] The same as LOGARITHMICALLY (q. v.).