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" The logarithm of a quotient is equal to the logarithm of the dividend diminished by the logarithm of the divisor. "
Plane and Spherical Trigonometry ... - Page 21
by Henry W. Jeans - 1842
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An Elementary Treatise on Algebra

Bewick Bridge - Algebra - 1818 - 254 pages
...the logarithm of =x— a;""=log. a'— log. a""" Я = log. IV— log.ra; from hence it appears that " the logarithm of " the quotient of any two numbers is equal to the difference of (N\ — ) " is equal to the logarithm of its numerator minus the logarithm " of its denominator."...
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A Treatise on the Elements of Algebra

Bewick Bridge - Algebra - 1821 - 648 pages
....'. the logarithm of _ =x- x""=log. a*-log. of"" n = log. N— log. n ; from hence it appears that " the logarithm of " the quotient of any two numbers is equal to the difference of lN\ " their logarithms; and that the logarithm of a. fraction ( — J " is equal to the...
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A Treatise on Algebra

George Peacock - Algebra - 1830 - 732 pages
...Log' — ; = log' n — log' n', or the logarithm of the n quotient of two numbers or quantities, is the logarithm of the dividend diminished by the logarithm of the divisor, and conversely. (3) Log' np=p log' n, or the logarithm of the pA, or any power of a number is found...
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Mathematical and Astronomical Tables: For the Use of Students in Mathematics ...

William Galbraith - Astronomy - 1834 - 454 pages
...therefore, N the logarithm of — =x — .r^log. r* — log. r^=log. N — log. n ; hence it appears, that the logarithm of the quotient of any two numbers is equal to the difference of their logarithms ; and that the logarithm (N\ — j is equal to the logarithm of its...
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A system of popular trigonometry

George Darley - 1835 - 142 pages
...logarithm of the product of any two numbers is equal to the sum of their logarithms, ibid. ART. 4. The logarithm of the quotient of any two numbers is equal to the difference of their logarithms, 7ART. 5. The logarithm of the power of any number is equal to the logarithm...
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An Elementary Treatise on Algebra: To which are Added Exponential Equations ...

Benjamin Peirce - Algebra - 1837 - 302 pages
...diminished by the logarithm of the other factor ; or, in other words, The logarithm of the quotient is equal to the logarithm of the dividend, diminished by the logarithm of the divisor. 12. Corollary. We have, by arts. 11 and 7, log. - = log. 1 — log. n IV =. — log. n ; that is, the...
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An Elementary Treatise on Algebra: To which are Added Exponential Equations ...

Benjamin Peirce - Algebra - 1837 - 300 pages
...diminished by the logarithm of the other factor ; or, in other words, The logarithm of the quotient is equal to the logarithm of the dividend, diminished by the logarithm of the divisor. 12. Corollary. We have, by arts. 11 and 7, log. - = log. 1 — log. n TC .i = — log. n ; that is,...
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A Treatise on the Elements of Algebra

Bewick Bridge - Algebra - 1839 - 280 pages
...logarithm of — — x — x""=log. a* — log. at""= log. N — log. n ; from hence it appears that " the logarithm of the quotient of any two numbers is equal to the difference of their N logarithms ; and that the logarithm of a fraction — is equal to the logarithm...
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An Elementary Treatise on Algebra, in Theory and Practice: With Attempts to ...

John D. Williams - Algebra - 1840 - 634 pages
...=а*-*.. .'. Log. — =x — x by the definition of lona*, ' n , J garithms, =log.N — log.ra. 124. Hence the logarithm of the quotient of any two numbers is equal to the difference of the logarithm of those numbers. If N be less than и, a; is less than x ; .•. therefore...
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A Treatise on Algebra: Embracing, Besides the Elementary Principles, All the ...

George Roberts Perkins - Algebra - 1842 - 370 pages
...respective logarithms ; and (Art. 218) the logarithm of the quotient of one quantity divided by another is equal to the logarithm of the dividend diminished by the logarithm of the divisor, we find for the logarithm of our expression 3.75X1.06 log. - - =log. 3.75+log. 1.06-log. 365. By the...
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