 | Elias Loomis - Logarithms - 1859 - 372 pages
...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 - 482 pages
...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 - Algebra - 1864 - 386 pages
...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 - Logarithms - 1865 - 232 pages
...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 - Navigation - 1867 - 506 pages
...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 =... | |
 | Robert Wallace - 1870 - 164 pages
...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 - Geometry - 1871 - 302 pages
...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 - Algebra - 1874 - 446 pages
...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"... | |
 | Carl Bremiker - Logarithms - 1875 - 544 pages
...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 - Arithmetic - 1876 - 389 pages
...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... | |
| |
Ios- y" &cFrom which it is evident, that the logarithm of the product of any number of factors is equal to the sum of the logarithms of those factors. Hence... 
