| John Bonnycastle - Algebra - 1813 - 456 pages
...a1'1' '=•-,; and by the definition of logarithms, x — x' = log. ~, or log. y- log. y = log. ^. Hence the logarithm of a fraction, or of the quotient...logarithm of the denominator. And if each member of the equation a* = y be raised to the fractional power -, we shall have a" = y" ; and consequently, as before,... | |
| James Ryan - Algebra - 1824 - 550 pages
...powers, — , or a =— ,; and by the definition of logarithms, x— x'=\og. lJ ; or log. y— log. y'— Hence the logarithm of a fraction, or of the quotient...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... | |
| James Ryan, Robert Adrain - Algebra - 1824 - 542 pages
...and by the definition of ay logarithms, a;— a;'=log. \- ; or log. y— log. y'= log. (*-, tr ^ ; Hence the logarithm of a fraction, or of the quotient...the logarithm of the numerator minus the logarithm «f the denominator. 508. And if each member of the equation, a*=y, m be raised to the fractional power... | |
| John Bonnycastle - Algebra - 1825 - 336 pages
...logarithms, laid down in the first part of this article, x— x =log.— or y log.-,— log. y— log. y'. Hence the logarithm of a fraction, or of the quotient...denominator. And if each member of the common equation ar=^y be raised to the fractional power denoted by — , we shall m n3 have, in that case, o"«~3:=tyn... | |
| James Ryan - Algebra - 1826 - 430 pages
...of logarithms, x — a'=log. -T~ 5 or log. 3, -log. y'= log. Hence the logarithm of a fraction, ur of the quotient arising from dividing one number by another, is equal to the logarithm oj the numerator minus the logarithm of the. denominator. • 508. And if each member of the equation,... | |
| 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 -... | |
| William Smyth - Algebra - 1830 - 278 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. 216. If in the equation... | |
| Adrien Marie Legendre - Geometry - 1836 - 394 pages
...hence 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... | |
| Adrien Marie Legendre - Geometry - 1837 - 376 pages
...hence it would have been more exact -o have added the former number. The logarithm of a vulgar fraction is equal to the logarithm of the numerator, minus the logarithm of the denominator. The logarithm of a decimal fraction is found, by considering it as a whole number, and then prefixing... | |
| Charles Davies - Navigation - 1837 - 342 pages
...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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