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" ... the logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator. "
A Treatise on Algebra ... - Page 242
by William Smyth - 1861
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A Treatise on Algebra, in Practice and Theory: With Notes and ..., Volume 1

John Bonnycastle - Algebra - 1813 - 456 pages
...Hence the logarithm of a fraction, or of the quotient arising from dividing one number by another, is equal to the logarithm of the numerator minus the logarithm of the denominator. And if each member of the equation a* = y be raised to the fractional power -, we shall have a" = y"...
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An Introduction to Algebra: With Notes and Observations : Designed for the ...

John Bonnycastle - Algebra - 1818 - 284 pages
...Hence the logarithm of a fraction, or of the quotient arising from dividing one number by another, is equal to the logarithm of the numerator minus, the logarithm of the denominator. And if each member of the common equation ax=y be raised to the fractional power denoted by — , we...
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An Elementary Treatise on Algebra: Theoretical and Practical

James Ryan - Algebra - 1824 - 550 pages
...Hence the logarithm of a fraction, or of the quotient arising from dividing one number by another, is equal to the logarithm of the numerator minus the logarithm of the denominator. 508. And if each member of the equation, ax=y. m be raised to the fractional power «, we shall have...
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An Introduction to Algebra: With Notes and Observations, Designed for the ...

John Bonnycastle - Algebra - 1825 - 336 pages
...Hence the logarithm of a fraction, or of the quotient arising from dividing one number by another, is equal to the logarithm of the numerator minus the logarithm of the denominator. And if each member of the common equation ar=^y be raised to the fractional power denoted by — ,...
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The steam engine theoretically and practically displayed, by G. Birkbeck and ...

George Birkbeck - 1827 - 166 pages
...these conditions in the above general formula, and bearing in mind that the logarithm of a fraction is equal to the logarithm of the numerator, minus the logarithm of the denominator, we shall have the three following equations of conditions : - 0 4259687 = 25 o + 635 b + 15625 c -...
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Elements of Algebra

William Smyth - Algebra - 1830 - 278 pages
...log 35 = log 5 -f- log 7 ; having already calculated the logarithms of 5 and 7, the logarithm of 37 will be found therefore by adding the logarithm of...place in the tables the logarithms of entire numbers. 216. If in the equation 10x=y we make successively * = 0, 1, 2, 3, 4 ... we have .9.= !, 10, 100, 1000,...
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Elements of Algebra

William Smyth - Algebra - 1833 - 288 pages
...the logarithm of 35, for example, we have 35 = 5 X 7 ; whence log 35 = log 5 + log 7; having already calculated the logarithms of 5 and 7, the logarithm...logarithms are calculated to 4 places of decimals. 202. The most convenient number for a base to a system of logarithms, and the one employed in the construction...
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Elements of Algebra

William Smyth - Algebra - 1836 - 288 pages
...the logarithm of 35, for example, we have 35 = 5 X 7; whence log 35 = log 5 + log?; having already calculated the logarithms of 5 and 7, the logarithm...we have a table of logarithms of numbers from 1 to 39 inclusive, the base of the system is 2, and the logarithms are calculated to 4 places of decimals....
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1836 - 394 pages
...it would have been more exact lo have added the former number. The logarithm of a vulgar fraction is equal to the logarithm of the numerator, minus the logarithm of the denoroinator. The logarithm of a decimal fraction is found, by considering it as a whole number, and...
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Elements of Surveying: Including a Description of the Instruments and the ...

Charles Davies - Navigation - 1837 - 342 pages
...fraction is equal to the quotient obtained by dividing the numerator by the denominator, its logarithm will be equal to the logarithm of the numerator minus the logarithm of the denominator. Therefore, log yTy=log 3678— log 100 = 3.565612—2 = 1.565612 from which we see, that a mixed number...
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