| Dana Pond Colburn - 1858 - 276 páginas
...8427 29. .0049 80. 73648 31. 4957.3 X 300. 32. 2796 X 8000. 50* Multiplication by Large Numbers. (a.) **The product of two numbers is equal to the sum of the** products obtained by multiplying one of them by the parta into which the other may be divided. (See... | |
| James B. Dodd - 1859 - 306 páginas
...then and, by substituting these values in the last logarithmic equation, we have, considering that **the logarithm of a quotient is equal to the logarithm of the dividend** minus the logarithm of the divisor, log. (»+i>- log. B=2ar(^+^^+-pL—5.+fa,. ;)or log (w+1)= log.... | |
| Joseph Allen Galbraith - 1860
...which the rules for using logarithmic tal1ies in numerical computations are derived. PROPOSITI°N I. **The logarithm of the product of two numbers is equal to the sum of the logarithms of the numbers.** If the numbers be N and M, let n = log N, and m = log M to any base a, then by the definition, By multiplication,... | |
| Joseph Allen Galbraith, Samuel Haughton - 1860 - 252 páginas
...which the rules for using logarithmic tables in numerical computations are derived. PROPOSITION I. **t'he logarithm of the product of two numbers is equal to the sum of** e logarithms of the numbers. If the numbers be N and M, let n = log N, and m = log Л/ to any ise a,... | |
| Charles Davies - 1860 - 400 páginas
...since a is the base of the system, we have from the definition, 3/ + x" = log (N' x N") ; that is, **The logarithm of the product of two numbers is equal to the** tum of their logarithms. 231 • If we divide equation (1) by equation (2), member by member, we have,... | |
| T. Percy Hudson - 1862 - 184 páginas
...is called the logarithm of N with reference to a, or, as it is usually expressed, to the base a. 2. **The logarithm of the product of two numbers is equal to the sum of the logarithms of the numbers.** Let a be the base, M, N the numbers, and x and y their logarithms respectively to the base a. Then... | |
| Horatio Nelson Robinson - 1863 - 420 páginas
...unity. For, let a* = a; then x = log. a. But by (88), if a' = a, then x = 1, or log. a = 1. 3. — **The logarithm of the product of two numbers is equal to the sum of the logarithms of the** two numbers. For, let m = a*, n = a"; then x = log. от, z = log. n. But by multiplication we have... | |
| Lefébure de Fourcy (M., Louis Etienne) - 1868 - 288 páginas
...y1 + log y", &c. = log (y + tf + f, &c.) (2) Therefore, the logarithm of the product of two or more **numbers is equal to the sum of the logarithms of the numbers** forming the product. 10. If we divide two of the equations (1), member by member, we have a1~* = y-:... | |
| Charles Davies - 1871 - 431 páginas
...(5), member by member, we have, 10" +q = mn; whence, by the definition, p + q = log (mn) (6.) That is, **the logarithm of the product of two numbers is equal to the sum of the logarithms of the numbers.** 6. Dividing (4) by (5), member by member, we have, whence, by the definition, 10*- = -; n P ~ 9 = That... | |
| Adrien Marie Legendre - 1871 - 187 páginas
...we have, 10 = mn ; whence, by the definition, x + y = log (mn) (6.) That is, the logarithm of tJie **product of two numbers is equal to the sum of the logarithms of the numbers.** 6. Dividing ( 4 ) by ( 5 ), member by member, we have, whence, by the definition, «-y = "*(£) ........ | |
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