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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 90
av Robert Hamilton Pinkerton - 1884 - 176 sider
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## The Complete Practical Arithmetician: Containing Several New and Useful ...

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...
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## An Algebra Upon the Inductive Method of Instruction

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....
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## Binomial Theorem and Logarithms: For the Use of the Midshipmen at the Naval ...

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...
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## The United States Arithmetic: Designed for Academies and Schools

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...
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## Mathematics for practical men

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...
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## The First Part of the United States Arithmetic: Designed for Schools

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...
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## The scholar's guide to arithmetic; or, A complete exercise-book

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,...
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## Manual of plane trigonometry, by J.A. Galbraith and S. Haughton

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....
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## The Millwright and Engineer's Pocket Companion

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...
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## Algebra for High Schools and Colleges: Containing a Systematic Exposition ...

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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