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" I. The logarithm of a product equals the sum of the logarithms of the factors. "
A Treatise on Plane and Spherical Trigonometry - Page 100
by Ephraim Miller - 1894 - 193 pages
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A Treatise on the Differential and Integral Calculus

Théodore Strong - Calculus, Integral - 1869 - 640 pages
...may be called logarithms of 1 + a, 1 + b, and of their product. Hence, in any system of logarithms, the logarithm of a product equals the sum of the logarithms of its factors ; reciprocally, the logarithm of a quotient equals the logarithm of Hie dividend, minus that of the...
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A College Algebra

James Morford Taylor - Algebra - 1889 - 400 pages
...; .-. loga i = 0. 302. The logarithm of the base itself is I . For a1 — a; .-. \ogaa — 1. 303. The logarithm of a product equals the sum of the logarithms of its factors. Let log, M = x, log„ N=y; then M=a', N—ay. §299. Therefore MN=a*+y. Hence log, (MN) = x + y =...
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Higher Algebra: A Sequel to Elementary Algebra for Schools

Henry Sinclair Hall, Samuel Ratcliffe Knight - Algebra - 1891 - 606 pages
...(M') / 207. It follows from the results we have proved that (1) the logarithm of a product is equal to the sum of the logarithms of its factors ; (2) the logarithm of a fraction is equal to the logarithm of the numerator diminished by the logarithm of the denominator...
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Elements of Trigonometry with Logarithmic and Other Tables

Henry Hunt Ludlow - Logarithms - 1891 - 322 pages
...table beyond 1000.) GENERAL PROPERTIES OF LOGARITHMS. 4. i °. The logarithm of any product is equal to the sum of the logarithms of its factors. 2°. The logarithm of any quotient is equal to the logarithm of the dividend minus that of the divisor. 3°. The logarithm...
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An Academic Algebra

James Morford Taylor - Algebra - 1893 - 362 pages
...For a°=l. .-. logal=0. 335. The logarithm of the base itself is 1. For а' = a. .-. logaa = 1. 336. The logarithm of a product equals the sum of the logarithms of its factors. For let M= a*, N— a» ; then MXN= aI+*. Hence loga(3f x N) = x + y = loga3f + logaN. 337. TJle logarithm...
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Elementary Trigonometry

Henry Sinclair Hall, Samuel Ratcliffe Knight - Plane trigonometry - 1893 - 434 pages
...log0(Jfr) = 159. It follows from the results we have proved that (1) the logarithm of a product is equal to the sum of the logarithms of its factors ; (2) the logarithm of a fraction is equal to the logarithm of the numerator diminished by the logarithm of the denominator...
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Elementary Algebra

Henry Sinclair Hall, Samuel Ratcliffe Knight - Algebra - 1895 - 508 pages
...logjax log„Z> = l. 414. In Arts. 403-405 we demonstrated, (1) The logarithm of a product is equal to the sum of the logarithms of its factors. (2) The logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator. (3) The...
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Plane Trigonometry

Elmer Adelbert Lyman, Edwin Charles Goddard - Plane trigonometry - 1899 - 188 pages
...40. Fгoт the definition it follows that the laws of indices apply to logarithms, and we have : I. The logarithm of a product equals the sum of the logarithms of the factors. II. The logarithm of a quotient equals the logarithm of the dividend minus the logarithm...
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Plane and Spherical Trigonometry

Elmer Adelbert Lyman, Edwin Charles Goddard - Trigonometry - 1900 - 228 pages
...log^l. 40. From the definition it follows that the laws of indices apply to logarithms, and we have : I. The logarithm of a product equals the sum of the logarithms of the factors. II. The logarithm of a quotient equals the logarithm of the dividend minus the logarithm...
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College Algebra

Leonard Eugene Dickson - Algebra - 1902 - 242 pages
...the three laws of indices (exponents) give rise to three corresponding properties of logarithms. I. The logarithm of a product equals the sum of the logarithms of its factors. Let the factors be N and M. By the definition (4) we have (5) N=aiog.N, M=alog**. Hence, by the first...
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