| Thomas Jephson - Calculus - 1826
...'Va/ series. Hence /. 10 = '9 + -'- x ('9)2 4- fx ('9)3 + &c. = 2-302585093, £c. 23. ÏVze logarithm **of the product of two numbers is equal to the sum of their** logarithms, and the logarithm of the quotient is equal to the difference of their logarithms. Letj/... | |
| Andrew Bell (writer on mathematics.) - 1839
...in this system 2 = 14, 3 = 18, 4 = 116. . GENERAI, PROPERTIES OF LOGARITHMS. (501.) 1 The logarithm **of the product of two numbers is equal to the sum of** the logarithms of these numbers.1 For let aх = y, and aх, .= y', then for the base a, x = ly, and... | |
| Joseph Allen Galbraith - 1852
...multiply these, NX M= 1o**™; therefore, log NX M—n + m = log N + log if. PROPOSITION I. The logarithm **of the product of two numbers is equal to the sum of** the logarithms of the numbers. If we divide the former of these equations by the latter N__ therefore... | |
| Great Britain. Committee on Education - Schools - 1855
...ARITHMETIC. (Two Hours allowed for this Paper,) Section 1. 1. Define a logarithm; and show that the logarithm **of the product of two numbers is equal to the sum of their** logarithms ; and the logarithm of their quotient, to the difference of their logarithms. 2. Show that... | |
| 1855
...of the Earth. LOGARITHMIC ARITHMETIc. SECT. I.— 1. Define a logarithm; and show that the logarithm **of the product of two numbers is equal to the sum of their** logarithms, and the logarithm of their quotient to the difference of their logarithms. 2. Show that... | |
| Joseph Allen Galbraith - 1860
...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... | |
| Joseph Allen Galbraith, Samuel Haughton - Mathematics - 1860 - 252 pages
...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,... | |
| T. Percy Hudson - Trigonometry - 1862 - 184 pages
...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... | |
| Horatio Nelson Robinson - Algebra - 1863 - 420 pages
...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... | |
| Charles Davies - Surveying - 1871 - 431 pages
...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,... | |
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