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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 Mathematicall Tables - Página viii
por Joseph Allen Galbraith, Samuel Haughton - 1860 - 252 páginas
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## The elements of algebra

Andrew Bell (writer on mathematics.) - 1839 - 502 páginas
...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 —...
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## Binomial Theorem and Logarithms: For the Use of the Midshipmen at the Naval ...

William Chauvenet - 1843 - 102 páginas
...them together ; the sum will be found in the table to be the logarithm of the required product. 61. The logarithm of the quotient of two numbers is equal to the difference of their logarithms. For b and c being any two numbers, we have a\og.b—l) alog.<;_cDividing the first...
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## Papers for the Schoolmaster, Volumen2

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,...
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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 PROPOSITION III. The logarithm...
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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...
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## Elements of Geometry and Trigonometry

Adrien Marie Legendre - 1852 - 436 páginas
...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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## 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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## 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...
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## Rudimentary Treatise on Logarithms

Henry Law - 1853 - 84 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 Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - 1854 - 436 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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