| ELIAS LOOMIS, LL.D. - 1859
...MULTIPLICATION BY LOGARITHMS. (11.) According to Art. 3, the logarithm of the product of two or more **factors is equal to the sum of the logarithms of those factors. Hence,** for multiplication by logarithms, we have the following RULE. Add the logarithms of the factors ; the... | |
| Olinthus Gregory - 1863
...it appears that in every system of logarithms, the logarithm p+p' of a product N N', composed of two **factors, is equal to the sum of the logarithms of those factors.** C. If we have any numbers A, is, c, D, how many soever, we may prove in a similar manner, that (using... | |
| Elias Loomis - 1864 - 359 sider
...of the base a which is equal to NN' ; hence PROPERTY I. The logarithm of the product of two or more **factors is equal to the sum of the logarithms of those factors. Hence** we see that if it is required to multiply two or more numbers by each other, we have only to add their... | |
| John Walmsley - 1865 - 182 sider
...of N to the base a. So that if ax = N, then x = Iog0 N ; or if x = Iog0 N, then aC =• N. 109. TJie **logarithm of the product of any number of factors is equal to the sum of the logarithms of** the factors. Let there be n factors of a number, namely, N,t N3, JVS, NH. Then it is required to prove... | |
| James Pryde - 1867 - 458 sider
...since a~co=— 05 = °í a therefore the logarithm of о = — oo ; that is, equals — infinity. 64. **The logarithm of the product of any number of factors...equal to the sum of the logarithms of those factors.** Let P, Q, R, S, be any quantities, and x, y, z, v, their logarithms to any base a ; then . •. x =... | |
| 1870
...yy'y"=log. y-(-log. y'-(-log y". F'rom which it is evident that the logarithm of the product of two or more **factors is equal to the sum of the logarithms of those factors.** (156.) Hence, if all the factors of a given number be supposed equal to each other, and the number... | |
| Elias Loomis - 1871 - 58 sider
...MULTIPLICATION BY LOGARITHMS. (11.) According to Art. 3, the logarithm of the product of two or more **factors is equal to the sum of the logarithms of those factors. Hence,** for multiplication by logarithms, wa have the following RULE. Add the logarithms of the factors ; the... | |
| Joseph Ficklin - 1874 - 418 sider
...like manner, (abc)n = a"ô"cn, and (abc . . . ¿)я = «"¿"с" . . . ¿". . • . TJie пл power **of the product of any number of factors is equal to the** product of the nth powers of those factors Again, (a")8 = «nx a" = a"+" = a2", (a")s = an x a" x a"... | |
| 1875 - 517 sider
...log .g=a—b, log Ac=ac, log VA=-, Hence we sec that the logarithm of a product of two factors (or **of any number of factors) is equal to the sum of the logarithms of** the two factors taken separately. Further, the logarithm of the quotient of one number divided by another... | |
| ROBERT POTTS - 1876
...it may be shewn that the log a {w! . w a . w a . : . . } =logA + log a « 2 + log a % + . . . . Or **that the logarithm of the product of any number of^...factors,., is equal to the sum. of the logarithms of** the several factors. 3. PROP. To finti the logarithm of the quotient of two numbers. Here «i^« 10... | |
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