...АУЛ. iЬеHence, we shall find by calculation 0 = 2.302585093 And - = 0.434294484 с This last number is called the modulus of the system of logarithms whose base is 10. SECTION CXIX. Logarithms. Let us now see the application of the principles explained in the preceding...

...loga», and (6) becomes The factor - by which the series ("7) is multiplied is independent of n, and is called the modulus of the system of logarithms whose base is a. In the same manner the respective moduli of the systems whose bases are b, e, and 10, are __ __ = ,__...

...number и to base c, multiplied by the reciprocal of the logarithm of a to base c. This multiplier is called the modulus of the system of logarithms whose base is a. Por the logarithms of all numbers calculated to base с are converted into logarithms of the same number...

...constant, nx' may be any number. Hence, in general, d(log-y) = m— , in which m У is a constant.* The constant m is called the Modulus of the system of logarithms whose base is a. 35. Let m and m' be the moduli of two systems of logarithms whose bases are « and b respectively....

...constant, и z' denotes any number; hence (5) holds true for all values of у, т being a constant. The constant m is called the Modulus of the system of logarithms whose base is a. Hence, the differential of the logarithm of a variable is equal to the modulus of the system into the...

...which the ratio ('logy' -'log y)/(y'— y) approaches when y' and y both approach the common limit 1 is called the modulus of the system of logarithms whose base is b. Let y' = ry ; then this ratio becomes 'log r and when y = ~L it is (blogr)/(r — 1).* Hence the...

...constant, mj' denotes any number ; hence (6), or [5], holds true for all values of и, т being a constant. The constant m is called the modulus of the system of logarithms whose base is a. The modulus of the common system of logarithms, obtained in § 97, is 0.434294 • • -. From the...

...number must be multiplied to obtain the logarithm of the same number in the system whose base is a, is called the modulus of the system of logarithms whose base is «. In the common system a = 10, aud 1 = .43429448. Hence Iog10 (1 + y) = .43429448 log. (1 + y). EXAMPLE...

...i) log,a = .— Ц . , log„6 that is, logbu and logj) are reciprocals. The constant multiplier ¡i is called the modulus of the system of logarithms whose base is b with reference to the system whose base is a. 36. Natural or Hyperbolic Logarithms. Theoretically...

...positive number. Hence (6) or [VIII0] holds true for all positive values of x, m being a constant. The constant m is called the modulus of the system of logarithms, whose base is denoted by b in this derivation. The general base is often denoted by a. The system whose modulus^is...