...logarithm of any number in that system by the Neperian logarithm of the same number; and, conversely, the logarithm of a number in any system is equal to the product of its Neperian logarithm by the modulus of the system, * To the series here investigated,...

...By taking nine terms of this series, we find a=2.718282, which is the base of Napier's system. 427. The logarithm of a number in any system is equal to...multiplied by the Naperian logarithm of the number. If we designate Naperian logarithms by Nap. log., and logarithms in any other system by log., then,...

...logarithms in the Naperian table by 0.43429 . . . In fact, it may be noted generally, that (Art. 76) The logarithm of a number in any system is equal to...multiplied by the Naperian logarithm of the number. 81. The natural number answering in the table of the common logarithms to 0.43429 ... is 2.718281828...

...a=e" hence p==esm=en wherefore n 1 n=sm or in=-=—n but — is the modulus of the system, and hence The logarithm of a number in any system is equal to the Naperian logarithm of that number multiplied by the modulus of the system. This property is not peculiar...

...n a=e* hence wherefore n 1 =^sm or- ,«=—-— » but — is the modulus of the system, and hence The logarithm of a number in any system is equal to the Naperian logarithm of that number multiplied by the modulus of the system. This property is not peculiar...

...the same number in different systems are to each other as the moduli of those systems; and also, that the logarithm of a number in any system is equal to the Naperian logarithm of the same number into the modulus of the given system. Сов. 2. — Dividing...

...systems. COR. 2. If, in (11) of Cor. 1, we let a'=e, we have m'= 1, and logay = mlogy. (12) Hence, the logarithm of a number in any system is equal to the Naperian logarithm of the same number multiplied by the modulus ofthat system. COR. 3. If, in (12)...

...reciprocal of the Napierian logarithm of its base. 321. From (2) and (3) of § 320 we have log, N= m log, N. That is, the logarithm of a number in any system is equal to the Napierian logarithm of the same number multiplied by the modulus of that system. 322. Value of M. If...

...base of that system. Modulus of Naperian system =1s. log,, of e = 1. The logarithm of a number (n) in any system is equal to the modulus of that system...multiplied by the Naperian logarithm of the number. Or: Modulus of common system = • 1s.log/ of 10 = 0.434294481903252. Logic n = modulus (comm~n system)...

...-= 1 . Modulus of common system - 1 + Ing, of 10 = 0.434294481903252. The logarithm of a number (n) in any system is equal to the modulus of that system...multiplied by the Naperian logarithm of the number. Or: Login та = modulus (common system) X log,, n. Log« n = modulus (Naperian system = 1 ) X log,...