 | Théodore Strong - 1869 - 640 σελίδες
...may be called logarithms of 1 + a, 1 + b, and of their product. Hence, in any system of logarithms, the logarithm of a product equals the sum of the logarithms of its factors ; reciprocally, the logarithm of a quotient equals the logarithm of Hie dividend, minus... | |
 | James Morford Taylor - 1889 - 400 σελίδες
...; .-. loga i = 0. 302. The logarithm of the base itself is I . For a1 — a; .-. \ogaa — 1. 303. The logarithm of a product equals the sum of the logarithms of its factors. Let log, M = x, log„ N=y; then M=a', N—ay. §299. Therefore MN=a*+y. Hence log, (MN)... | |
 | James Morford Taylor - 1893 - 362 σελίδες
...For a°=l. .-. logal=0. 335. The logarithm of the base itself is 1. For а' = a. .-. logaa = 1. 336. The logarithm of a product equals the sum of the logarithms of its factors. For let M= a*, N— a» ; then MXN= aI+*. Hence loga(3f x N) = x + y = loga3f + logaN.... | |
 | Ephraim Miller - 1894 - 222 σελίδες
...mantissa. The characteristic is integral, and the mantissa decimal. 142. Properties of Logarithms. (1) The logarithm of a product equals the sum of the logarithms of its factors. (2) The logarithm of a quotient equals the difference between the logarithm of the dividend... | |
 | Elmer Adelbert Lyman, Edwin Charles Goddard - 1899 - 188 σελίδες
...40. Fгoт the definition it follows that the laws of indices apply to logarithms, and we have : I. The logarithm of a product equals the sum of the logarithms of the factors. II. The logarithm of a quotient equals the logarithm of the dividend minus the logarithm of the divisor.... | |
 | Elmer Adelbert Lyman, Edwin Charles Goddard - 1900 - 228 σελίδες
...log^l. 40. From the definition it follows that the laws of indices apply to logarithms, and we have : I. The logarithm of a product equals the sum of the logarithms of the factors. II. The logarithm of a quotient equals the logarithm of the dividend minus the logarithm of the divisor.... | |
 | Leonard Eugene Dickson - 1902 - 242 σελίδες
...the three laws of indices (exponents) give rise to three corresponding properties of logarithms. I. The logarithm of a product equals the sum of the logarithms of its factors. Let the factors be N and M. By the definition (4) we have (5) N=aiog.N, M=alog**. Hence,... | |
 | John Marvin Colaw - 1903 - 444 σελίδες
...established and applied in the articles which immediately follow. 478. Computations by Logarithms. The logarithm of a product equals the sum of the logarithms of the factors. Thus, 100 x 1000 = 102 x 103 = 106. .'. log (100 x 1000) = 2 + 3 = log 100 + log 1000. In general,... | |
 | Elmer Adelbert Lyman - 1905 - 270 σελίδες
...Thus, 3.7993 = 7.7993 - 10. 339. The principles used in working with logarithms are as follows : I. The logarithm of a product equals the sum of the logarithms of the factors. II. The logarithm of a quotient equals the logarithm of the dividend minus the logarithm of the divisor.... | |
 | John Charles Stone, James Franklin Millis - 1905 - 776 σελίδες
...1. (Б) The logarithm of the base itself is 1 ; that is, %,,a = l. This follows from «' = «. ( C) The logarithm of a product equals the sum of the logarithms of its factors / that is, logamn = logum + log,¡n. To prove this, let ax=m, and a]l = n. Then nm=ax-a'J=ax+'J.... | |
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I. The logarithm of a product equals the sum of the logarithms of the factors. 
