| Thomas Jephson - 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/ = a1 and «/ — a*, therefore «/•«/'... | |
| Andrew Bell (writer on mathematics.) - 1839 - 498 páginas
...2* = 16, ... 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 - 80 páginas
...10m. If we 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
...or (J) a lava ; 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... | |
| Great Britain. Committee on Education - 1855
...during the reign of Mary. D LOGARITHMIC ARITHMETIC. (Two Hours allowed for this Paper,) Section 1. **1. Define a logarithm; and show that the logarithm...its number of integers. 3. One person out of 46 is** said to die every year in England, and one out of 34 to be born ; if there were no emigration, in how... | |
| Charles Davies - 1857 - 408 páginas
...since a is the base of the system, we have from the definition, x' + x" = log (Nt x N") ; that is, **The logarithm of the product of two numbers is .equal to the** turn of their logarithms. 231. If we divide equation (1) by equation (2), member by member, we have,... | |
| 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,... | |
| Joseph Allen Galbraith - 1860 - 304 páginas
...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... | |
| Charles Davies - 1860 - 412 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 - 200 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... | |
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