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" N .-. by definition, x — x" is the logarithm of ^ ; that is to say, The logarithm of a fraction, or of the quotient of two numbers, is equal to the logarithm of the numerator minus the logarithm of the denominator. III. Raise both members of equation... "
Higher Geometry and Trigonometry: Being the Third Part of a Series on ... - Page 81
by Nathan Scholfield - 1845 - 232 pages
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A Treatise on Algebra

Benedict Sestini - Algebra - 1857 - 258 pages
...or a*-* = - ; a* vv a" z z and consequently, x — y = I.-, that is, The logarithm of the quotient is equal to the logarithm of the numerator, minus the logarithm of the denominator. Raise to the exponent c both members of the equation a*= z, we will have (a 1 )' = z or a" = z,...
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Elements of Geometry and Trigonometry: From the Works of A.M. Legendre

Adrien Marie Legendre - Geometry - 1857 - 444 pages
...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 is 1, tf'e logarithm...
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A Treatise on Algebra: For the Use of Schools and Colleges

William Smyth - Algebra - 1858 - 344 pages
...therefore by adding the logarithm of 5 to that of 7. Since moreover the logarithm of a fraction will be equal to the logarithm of the numerator minus the logarithm of the denominator, it will be sufficient to place in the tables the logarithms of entire numbers. 201. Below we have a...
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Algebra for High Schools and Colleges: Containing a Systematic Exposition ...

James B. Dodd - Algebra - 1859 - 368 pages
...(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...
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Treatise on Algebra

Charles William Hackley - Algebra - 1864 - 530 pages
...that is to say, The logarithm of a fraction, or of the quotient of two numbers, is equal to tht • logarithm of the numerator minus the logarithm of...denominator. III. Raise both members of equation (1) to the nth power. N"=o". .-. by definition, nx is the logarithm of № ; that is to say, The logarithm of...
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Ray's Algebra, Part Second: An Analytical Treatise, Designed for ..., Part 2

Joseph Ray - Algebra - 1852 - 420 pages
...to a form in which it shall also be divisible by the same factor. Since the logarithm of a fraction is equal to the logarithm of the numerator, minus the logarithm of the denominator (Art. 361), therefore, . log. (l+x)- log. (l+z)= log. ( 1? ) . But, by division, we find 'x=l-\-xz...
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A Treatise on Algebra

Elias Loomis - Algebra - 1868 - 386 pages
...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 by member, we shall...
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Surveying and Navigation, with a Preliminary Treatise on Trigonometry and ...

Aaron Schuyler - Measurement - 1864 - 506 pages
...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 = x. Let ] ( (2)...
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Elementary Algegra

Daniel Barnard Hagar - Algebra - 1873 - 278 pages
...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 equation a" =...
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Plane and Spherical Trigonometry and Mensuration

Aaron Schuyler - Measurement - 1875 - 276 pages
...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. Г (1) b" = m; then, by def., log m = x. Let i. (_ (2)...
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