The logarithm of the product of two or more numbers is equal to the sum of the logarithms of the numbers. For, let m and n be two numbers, and x and y their logarithms. Then, by the definition of a logarithm, m — ax, and n = a". Elementary text-book of trigonometry - Side 90av Robert Hamilton Pinkerton - 1884 - 176 siderUten tilgangsbegrensning - Om denne boken
| Thomas Keith - 1822 - 332 sider
...their difference, will give the less number. 7. The quotient, arising from tlie division of tbe sum **of two, or more, numbers, is equal to the sum of the** quotients arising from tha division of the parts, separately, by the iame divisor. „ 8. If any two... | |
| John Hopkins Harney - 1840 - 288 sider
...immediately seen. This can often be done by re-solving the number into two or more factors, for the root **of the product of two or more numbers is equal to the** product of the roots of those numbers. It is required to find the second root of 196. 4 X 49 = 196.... | |
| William Chauvenet - 1843 - 92 sider
...power to which a must be raised in order to produce b. • PROPERTIES OP LOGARITHMS IN GENERAL. 60. **The logarithm of the product of two or more numbers is equal to the sum of the logarithms of** those numbers. For let b, c, d, &c. be any numbers, and a the base of any system of logarithms, then... | |
| William Vogdes - 1847 - 256 sider
...half their difference, will give the less number. The quotient, arising from the division of the sum **of two, or more numbers, is equal to the sum of the** quotients arising from the division of each number separately, by the same divisor. If any two numbers... | |
| Olinthus Gilbert Gregory - 1848 - 80 sider
...for multiplying powers, (page 50,) r1 x r'' = r1 * '> = N x N, ; and NN, . Ns =r' + 'i + '». Or tfte **logarithm of the product of two or more numbers, is equal to the sum of the** logaritltms of those numbers; and conversely, the logarithm of the quotient of ttco numbers, is equal... | |
| William Vogdes - 1849
...half their difference, will give the less number. The quotient, arising from the division of the sum **of two, or more numbers, is equal to the sum of the** quotients arising from the division of each number separately, by the same divisor. If any two numbers... | |
| John Bonnycastle - 1851
...their difference, will give the less number. 2. The quotient, arising from the division of the sum **of two or more numbers, is equal to the sum of the** quotients arising from the division of the parts, separately, by the same divisor. the question ; then,... | |
| Joseph Allen Galbraith - 1852
...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.... | |
| William Templeton - 1852
...half their difference, will give the less number. 2. The quotient arising from the division of the sum **of two or more numbers, is equal to the sum of the** quotients arising from the division of the parts separately, by the same divisor. 3. Any three of the... | |
| James B. Dodd - 1859 - 306 sider
...0 is the logarithm of 1, and in the second, 1 is the logarithm of a. Logarithm of a Product. (308.) **The Logarithm of the product of two or more numbers, is equal to the sum of the logarithms of** those numbers. In the equations ax=n and av=m, the exponents, x and y, are the logarithms of' n and... | |
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