| Joseph Allen Galbraith, Samuel Haughton - 1860 - 252 páginas
...from 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,... | |
| Thomas 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 = "*(£) ........ | |
| 1873 - 164 páginas
...(0.00130106) 2 ; <aooi30106 j,; 2.7 X (0.00130106)"- Use arithmetical complements in dividing. 6. Prove that **the logarithm of the product of two numbers is equal to the sum of the logarithms of the numbers.** 7. Find, by logarithms, the values of the following quantities (to six significant figures): ^(0.0126534);... | |
| Aaron Schuyler - 1873 - 482 páginas
...number corresponds to logarithm 3.63025? Ans. .0042683. MULTIPLICATION BY LOGARITHMS. 13. Proposition. **The logarithm of the product of two numbers is equal to the sum of** their logarithms. I! '(1) b• = m; then, by def., log m = a;. Let _ (2) b* = n; then, by def., log... | |
| Aaron Schuyler - 1864 - 490 páginas
...number corresponds to logarithm 3.63025? Am. .0042683. MULTIPLICATION BY LOGARITHMS. 13. Proposition. **The logarithm of the product of two numbers is equal to the** siim of their logarithms. C (1) b- = in; then, by def., log m=x. Let 1 (_ (2) b* = n; then, by def.,... | |
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