| Thomas Jephson - Calculus - 1826 - 472 pages
...'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 - 500 pages
...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 - 84 pages
...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... | |
| University of Sydney - 1853 - 810 pages
...or (<•) hypabyssal ; or (rf) plutonic ? MATHEMATICS I. FIRST PAPER. 1. Explain why the logarithm of the product of two numbers is equal to the sum of the logarithms of the two numbers. Find 1 he cube root of 1002-5 and the fifth power of 1-025, using... | |
| 1855 - 264 pages
...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... | |
| Great Britain. Committee on Education - School buildings - 1855 - 976 pages
...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... | |
| Joseph Allen Galbraith - 1860 - 290 pages
...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 - Logarithms - 1860 - 310 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 - 218 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 - 432 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... | |
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