| 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.... | |
| Andrew Bell (writer on mathematics.) - 1839 - 500 pages
...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 x' = ly. And aх... | |
| Euclides - 1840 - 192 pages
...cases, which form the first four propositions of his Second Book. The first of them is as follows : **The product of two numbers is equal to the sum of the** products of one of them multiplied by the parts of the other. Thus, if 5 and 10 be the two numbers,... | |
| Joseph Allen Galbraith - 1852 - 84 pages
...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 N log -=n-ra = logAT-log M.... | |
| University of Sydney - 1853 - 810 pages
...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 your tables, and compare... | |
| William Frederick Greenfield - 1853 - 228 pages
...the sum of the products of each part of the multiplicand and multiplier 127 PKOP. 8.— To prove that **the product of two numbers is equal to the sum of the** products of the multiplicand by each part, of the multiplier . 127 PROP. 9. — To prove the Rule for... | |
| Great Britain. Committee on Education - School buildings - 1855 - 976 pages
...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 - 264 pages
...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 - Algebra - 1857 - 408 pages
...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,... | |
| Dana Pond Colburn - 1858 - 288 pages
...8427 29. .0049 80. 73648 31. 4957.3 X 300. 32. 2796 X 8000. 50* Multiplication by Large Numbers. (a.) **The product of two numbers is equal to the sum of the** products obtained by multiplying one of them by the parta into which the other may be divided. (See... | |
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