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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. "
Binomial Theorem and Logarithms: For the Use of the Midshipmen at the Naval ... - Página 50
por William Chauvenet - 1843 - 92 páginas
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The elements of algebra

Andrew Bell (writer on mathematics.) - 1839
...and x' = ly. And aх x aх = yy', or aх+х'=yy'; and hence x + x' = lyi/ or lytf = ly + ly'(502.) 1 The logarithm of the quotient of two numbers is equal to the difference of their logarithms.1 For ax -=- a* = - or e"' = -; and hence x — ж'= l ~, У У1 У' or l?L = ly — ty...
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Papers for the Schoolmaster

1852
...of the expansion of HJ (« + 4 )». SECT. IV.— 1. Define the logarithm of a number, and show that the logarithm of the quotient of two numbers is equal to the difference of their logarithms. 2. Shew that cos. (A — B) = cos. A cos. B + sin. A sin. B. 3. Shew that if a, b, c be the sides of...
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The English Journal of Education, Volumen6

1852
...term of the expansion of (fl8 + ^)\ SECTION IV. — 1. Define the logarithm of a number, and show that the logarithm of the quotient of two numbers is equal to the difference of their logarithms. 2. Show that Cos (A — B) = Cos A Cos B + Sin A Sin B. 3. Show that if a, b, c be the sides of a plane...
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Manual of plane trigonometry, by J.A. Galbraith and S. Haughton

Joseph Allen Galbraith - 1852
...former of these equations by the latter N__ therefore N log -=n-ra = logAT-log M. M PROPOSITION П. The logarithm of the quotient of two numbers is equal to the difference of the logarithms of the numbers. If we raise each side of the equation , N=1on to the power p, therefore...
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Elements of Surveying and Navigation: With Descriptions of the Instruments ...

Charles Davies - 1852 - 392 páginas
...Dividing equation (1) by equation (2), member by member, we have, MM 10m n = i^or, m — n = logjr: 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

A. M. LEGENDRE - 1852
...equation (1) by equation (2), member by member, we have, mn MM 10 -=_r~0r, ra — tt = 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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Public Education: As Affected by the Minutes of the Committee of Privy ...

Sir James Kay-Shuttleworth - 1853 - 500 páginas
...determine the middle term of the expansion of Section 4. 1. Define the logarithm of a number, and show that the logarithm of the quotient of two numbers is equal to the difference of their logarithms. 2. Show that Cos (A- 13) = Cos A Cos B + Sin A Sin B. 3. Show that if a, b, c be the sides of a plane...
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Rudimentary Treatise on Logarithms

Henry Law - 1853 - 68 páginas
...or, the sum of the logarithms of m and n is the logarithm of their product. PROPOSITION N. THEOREM. The logarithm of the quotient of two numbers is equal to the logarithm of the dividend, with the logarithm of the divisor subtracted from it. Let X and / denote...
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Elements of Surveying, and Navigation: With Descriptions of the Instruments ...

Charles Davies - 1854 - 322 páginas
...Dividing equation (1) by equation (2), member by member, we have, 10m~n = -^or, m — n~logj^: 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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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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