| 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.... | |
| Andrew Bell (writer on mathematics.) - 1839 - 502 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
...N= ID", M= 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... | |
| Joseph Allen Galbraith - 1854
...solely on the position of the decimal point. PROPERTIES OF LOGARITHMS. 2. We shall now demonstrate four **propositions from which the rules for using logarithmic...PROPOSITION I. The logarithm of the product of two numbers** ie equal to the sum of fhf logarithme of the numbers. If the numbers be N and M, let я = log N, and... | |
| Great Britain. Committee on Education - 1855
...LOGARITHMIC 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... | |
| 1855
...annual motion 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... | |
| 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 - 1860
...from 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,... | |
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