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" The logarithm of . the quotient of two numbers, is equal to the logarithm of the dividend diminished by the logarithm of the divisor. "
Elements of Geometry and Trigonometry from the Works of A.M. Legendre ... - Page 256
by Charles Davies - 1854 - 432 pages
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An Elementary Treatise on Algebra: To which are Added Exponential Ewquations ...

Benjamin Osgood Peirce - Algebra - 1855 - 288 pages
...diminished by the logarithm of the other factor ; or, in other words, The logarithm ft/ie quotient is equal to the logarithm of the dividend, diminished by the logarithm of the divisor. 14. Corollary. We have, by arts. 13 and 9, log. — = log. 1 — log. n = — log. n ; that is, the...
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Elements of Surveying, and Navigation: With Descriptions of the Instruments ...

Charles Davies - Navigation - 1857 - 393 pages
...Dividing equation (1) by equation (2), member by member, we have, MM 10 =д^ог, m — n = log -y: hence, The logarithm of the quotient of two numbers,...of any number by 10, will be greater by 1 than the logarithm of that number ; also, Ле logaritJim of the quotient of any number divided by 10, will...
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Elements of Geometry and Trigonometry: From the Works of A.M. Legendre

Adrien Marie Legendre - Geometry - 1857 - 444 pages
...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,...of the divisor. 5. Since the logarithm of 10 is 1, tf'e logarithm of the product of any number by 10, will be greater by 1 than the logarithm of that...
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Plane and spherical trigonometry. [With] Solutions of problems

Henry William Jeans - 1858
...in the product: thus, if x=ab, then log. a;=log. a+log. b (6) The logarithm of the quotient of any two numbers is equal to the logarithm of the dividend diminished by the logarithm of the divisor: thus, if x=aib, or -, then о log. a;=log. a — log. b If a;=-=-, then ae log. a;=log. a+log. 6+log....
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Algebra

Isaac Todhunter - Algebra - 1858 - 496 pages
...therefore m/n - aa* = a'+'; therefore log, mn - x + y = log. m + log„ n. 53G. The logarithm of a quotient is equal to the logarithm of the dividend diminished by the logarithm of the divisor. For let x — log. m, y = log. n ; therefore m = a', therefore — = — = a"~' : na? therefore log,...
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Algebra for High Schools and Colleges: Containing a Systematic Exposition ...

James B. Dodd - Algebra - 1859 - 306 pages
...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 av=m, we have az-v=n-^m...
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Algebra

Isaac Todhunter - 1860
...therefore, mn = a* a" = a" *s ; therefore, log. mn = x+y= log. m + log. n. 536. The logarithm of a quotient is equal to the logarithm of the dividend diminished by the logarithm of t/ie divisor. For let x = log. m, y = log. n ; therefore, m = a*, n = a" ; therefore, -=^ = a'-;...
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Elements of Geometry, and Plane and Spherical Trigonometry: With Numerous ...

Horatio Nelson Robinson - Geometry - 1860 - 453 pages
...quotient arising from the division of am by <*", is equal to ani~". Hence, the logarithm of a quotient is the logarithm of the. dividend diminished by the logarithm of the divisor. If it is required to raise a number denoted by as, to the fifth power, we write a, giving it ar exponent...
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Manual of Mathematicall Tables

Joseph Allen Galbraith, Samuel Haughton - Logarithms - 1860 - 252 pages
...= a' By multiplication, NX M = a*" therefore, log NX M = n + m = log N+ log M. PROPOSITION II. The logarithm of the quotient of two numbers is equal to the difference of the logarithms of the numbers. By diviaion. N — = a"~m M therefore N log — = n —...
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Manual of mathematical tables, by J.A. Galbraith and S. Haughton

Joseph Allen Galbraith - 1860
...By multiplication, ДГхЛГ =оnim therefore, log NX M = я + m = log N + log M. PROPoSITION II. The logarithm of the quotient of two numbers is equal to the difference of the logarithms of the numbers. By division. N — = an~m M therefore N log — = n -...
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