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N .•. def. (2), x— x1 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 (1) to...
An Introduction to Algebra, with Notes and Observations: Designed for the ... - Side 251
av John Bonnycastle - 1829 - 312 sider
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## The elements of algebra, with additions by W. Galbraith and W. Rutherford

John Bonnycastle - 1848
...PQKS = cf. af . a' . a" = a"+'+„ + „; hence log.PQBS = (2) The logarithm of a fractional quantity is equal to the logarithm of the numerator minus the logarithm of the denominator. Let a" = P and a* = Q, then x = }ogje and y = log.Q ; hence Q ~ u-- - ' .-. log,- — xy — log.P—...
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## BONNYCASTLE'S INTRODUCTION TO ALGEBRA; CONTAINING THE INDETERMINATE AND ...

JAMES RYAN - 1851
...Q% If ' down in the first part of this article, x — x' = log. -, or log. 2. = log. y - log. y'. y Hence, the logarithm of a fraction, or of the quotient...denominator. And if each member of the common equation a? — y be raised to the fractional power denoted by — , we shall have, m —x in that case, a n...
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## Ray's Algebra Part Second: An Analytical Treatise, Designed for High Schools ...

Joseph Ray - 1852 - 396 sider
...logarithm of the quotient. The same principle may be expressed otherwise thus, the logarithm of a fraction is equal to the logarithm of the numerator, minus the logarithm of the denominator. From this article, and the preceding, we see that by means of logarithms, the operation of Multiplication...
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## A Treatise on Algebra

Elias Loomis - 1855 - 316 sider
...equal to ^ ; hence, PROPERTY II. The logarithm of a fraction, or of the quotient of one number divided by another, is equal to the logarithm of the numerator, minus the logarithm of the denominator. Hence we see that if we wish to divide one number by another, we have only to subtract the logarithm...
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## NEW COMBINATIONS Binomial Cheorem and Logorithuis;

JOSEPH B. MOTT. - 1855
...log 6 = log^ — loga; therefore, log 2 = log p — log a : a that is, the logarithm of a fraction is equal to the logarithm of the numerator, minus the logarithm of the denominator. (THEOREM 2.) Or, for a more general theorem for fractions, let us resume the equation log ^ — log...
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## Treatise on Algebra, for the Use of Schools and Colleges

William Smyth - 1855 - 336 sider
...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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## A Treatise on Algebra

Benedict Sestini - 1857 - 216 sider
...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 Algebra: On the Basis of M. Bourdon, Embracing Sturm's and ...

Charles Davies - 1857 - 400 sider
...definition, v , (N' \ , • of — x" = log I -— 1 ; that is, The logarithm of the quotient which arises from dividing one number by another is equal to the logarithm of the dividend minus the logarithm of the divisor. 232i If we raise both members of equation (1) to the «'*...
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## A Treatise on Algebra: For the Use of Schools and Colleges

William Smyth - 1858 - 320 sider
...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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## Elements of Algebra: On the Basis of M. Bourdon, Embracing Sturm's and ...

Charles Davies - 1860 - 400 sider
........ w J5ut, from the definition. (N' \ -]yr)-> that is, The logarithm of the quotient which arises from dividing one number by another is equal to the logarithm of the dividend minus the logarithm of tin divisor. 232t If we raise both members of equation (1) to the nth...
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