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" The logarithm of the quotient is equal to the logarithm of the dividend, diminished by the logarithm of the divisor. "
An Elementary Treatise on Algebra: To which are Added Exponential Equations ... - Page 262
by Benjamin Peirce - 1837 - 284 pages
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Manual of Algebra

William Guy Peck - Algebra - 1875 - 348 pages
...have, whence, from the definition, x — y — Log ^; . . . . (6) hence, the following principle: 2°. The logarithm of the quotient is equal to the logarithm of the dividend diminished by that of the divisor. If we raise both members of (3) to any power denoted by p, we have, whence, by...
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Practical Treatise on the Differential and Integral Calculus: With Some of ...

William Guy Peck - Calculus - 1877 - 238 pages
...being a function of x, S and we have, after reduction, fs + ds\ ,,/iZs ds* ds3 . But the logarithm of a quotient, is equal to the logarithm of the dividend, diminished by the logarithm of the divisor; changing the form of the first member and suppressing all the terms in the second member, after the...
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Elementary Trigonometry

James Hamblin Smith - Trigonometry - 1877 - 244 pages
...treating of logarithms to the particular base 10, we may omit the suffix. 148. Tlie logarithm of a quotient is equal to the logarithm of the dividend diminished by the logarithm of the divisor. Let m=a*, and n=as. Then - = a-», •'• s. - = xy = Ioga m- log. »i. Thus tho operation of Division...
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New Practical Algebra: Adapted to the Improved Methods of Instruction in ...

James Bates Thomson - Algebra - 1878 - 322 pages
...numbers, m and n their logarithms, and b the base. Then 6»> = a And 6" = c Multiplying, &»+" = ae. 2°. The logarithm of the dividend diminished by the logarithm of the divisor is equal to the logarithm of the quotient of the two numbers. Let a and c denote any two numbers, m...
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The Collegiate Algebra: Adapted to Colleges and Universities

James Bates Thomson, Elihu Thayer Quimby - Algebra - 1880 - 360 pages
...numbers, m and n their logarithms, and b the base. Then frm = a And 6" = e Multiplying, 6™+" = ae. 2°. The logarithm of the dividend diminished by the logarithm of the divisor is equal to the logarithm of the quotient. Let a and с denote any two numbers, m and n their logarithms,...
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The Cambridge Examiner, Volume 3

Education, Higher - 1883 - 536 pages
...cosine of the sum of two angles whose sines and cosines are given. 3. Prove that the logarithm of a quotient is equal to the logarithm of the dividend diminished by the logarithm of the divisor. 4. Find log '005957964, having given log 59579 = 4-7750933, log 59580 = 4"7751005. 5. Prove that in...
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Elementary algebra. To which is now added an appendix

James Hamblin Smith - 1883 - 466 pages
...are treating of logarithms to the particular base 10, we may omit the suffix. 456. The logarithm of a quotient is equal to the, logarithm of the dividend diminished by the logarithm of the divisor. Let m=a', and n=a'. Then "ao"~'5 = log.m — log.n. Thus the operation of Division is changed into...
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Military examinations. Mathematical examination papers set at an open ...

Civil service commission - 1883 - 62 pages
...£ + - . ß aba / JS Sol. a + fl = • ' " «48 or + = + . QED 10. — Prove that the logarithm of a quotient is equal to the logarithm of the dividend diminished by the logarithm of the divisor. Given log. 2 = -69314718, log. 3 = 1-09861229 ; fiad the logarithms to base e of 8 /0\3e> /04 Д °/9"...
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Elementary text-book of trigonometry

Robert Hamilton Pinkerton - Trigonometry - 1884 - 194 pages
...of two or more numbers is equal to the sum of the logarithms of the numbers. II. The logarithm of a quotient is equal to the logarithm of the dividend diminished by the logarithm of the divisor; or (what is the same thing differently expressed) the logarithm of a fraction is equal to the logarithm...
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Elementary Algebra

Walter William Rouse Ball - Mathematics - 1890 - 512 pages
...tc + y + z + ... - loga m + loga n + \ogap + ... . 256. Logarithm of a Quotient. The logarithm of a quotient is equal to the logarithm of the dividend diminished by the logarithm of the divisor. Let m be the dividend, and let n be the divisor, and let n = a", .'. y = logan. m _ a* __ ry n a" =...
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