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" The logarithm of the quotient of two numbers is equal to the logarithm of the dividend minus the logarithm of the divisor. "
Manual of mathematical tables, by J.A. Galbraith and S. Haughton - Página ix
por Joseph Allen Galbraith - 1860
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Manual of plane trigonometry, by J.A. Galbraith and S. Haughton

Joseph Allen Galbraith - 1854
...multiplication, .2V x Ж = IOM*™; therefore, log .ZV x M = я + от = log .ЯГ+ log Ж PROPOSITION П. The logarithm of the quotient of two numbers is equal to the di/ennce of the logarithms of the numbers. By division, N F-»o—; therefore log — = я - m = log...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - 1854 - 432 páginas
...Dividing equation (1) by equation (2), member by member, we have, JO™ »BB_OTjW_Wesi0g— : hence, The logarithm of the quotient of two numbers, is equal to the logarithm of the dividend diminished by the logarithm of the divisor. 5. Since the logarithm of 10...
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Elements of Geometry and Trigonometry from the Works of A. M. Legendre ...

Adrien Marie Legendre, Charles Davies - 1857 - 432 páginas
...equation (1) by equation (2), member by member, we have, , , Jf J/ 10m~" = .^or, m — n = log.r^: hence, The logarithm of the quotient of two numbers, is equal to the logarithm of the dividend diminished by the logarithm of the divisor. 5. Since the logarithm of 10...
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Algebra for High Schools and Colleges: Containing a Systematic Exposition ...

James B. Dodd - 1859 - 306 páginas
...have y=nm (41), in which x-\-y is the logarithm of the product n m. Logarithm of a Quotient. (309.) The logarithm of the quotient of two numbers, is equal to the logarithm of the dividend minus the logarithm of the divisor. Dividing the Equation ax = n by the Equation...
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Manual of Mathematicall Tables

Joseph Allen Galbraith, Samuel Haughton - 1860 - 252 páginas
...definition, Ar = a» M = a'» By multiplication, NX M = a»*" therefore, log NX M = n + m = log N+ log M. PROPOSITION II. The logarithm of the quotient...the difference of the logarithms of the numbers. By diviaion. N — = a"~m M therefore N log — = n — m = log N — log M M PROPOSITION III. The logarithm...
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Algebra: Adapted to the Course of Instruction Usually Pursued in the ...

Paul Allen Towne - 1865 - 298 páginas
...numbers, J which is 5 + 4. 13S. Again, a* = M and a" = N M By dividing we have a** = — . That is, The logarithm of the quotient of two numbers is equal to the difference of their logarithms, Thus, the logarithm of 100000000000 is 11. The logarithm of 100000000 is 8. And the...
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The University Algebra

John Fair Stoddard, William Downs Henkle - 1866 - 528 páginas
...have aT+y—uz. PEO POSITION 5. (482.) In every system, the logarii~r.tr, of the quotient o/ t'joo numbers is equal to the difference of the logarithms of the numbers, since when cf—v, and a'— z wo have a*~'=-. I COR. — From these propositions we derive as a corollary...
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A TREATISE ON ALGEBRA

ELIAS LOOMIS, L.L.D. - 1868
...find the number corresponding to the resulting logarithm, and it will be the product required. 397. The logarithm of the quotient of two numbers is equal to the logarithm of the dividend diminished by that of the divisor. If we divide Eq. (1) by Eq. (2), member...
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Elementary Algegra

Daniel Barnard Hagar - 1873 - 263 páginas
...by the other, member by member, we have ax+'=mn, in which x+y is the logarithm of the product mn. 4. The logarithm of the quotient of two numbers is equal to the logarithm of the dividend diminished by that of the divisor. For, dividing the equation a? = m by the...
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Surveying and Navigation, with a Preliminary Treatise on Trigonometry and ...

Aaron Schuyler - 1864 - 490 páginas
...75831.667. 5. Find the product of 85, .097, and .125. Ans. 1.03062. DIVISION BY LOGARITHMS. 16. Proposition. The logarithm of the quotient of two numbers is equal to the logarithm of the dividend minus the logarithm of the divisor. (" (1) 6-= yn; then, by def., log TO...
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