 | John Bonnycastle - Algebra - 1818 - 284 pages
...-, ; and by the definition of logarithms, < y laid down, in the first part of this article, x—x,= log. . . Hence the logarithm of a fraction, or of...logarithm of the denominator. And if each member of the common equation ax=y be raised to the fractional power denoted by — , we shall mm have, in that case,... | |
 | John Bonnycastle - Algebra - 1818 - 326 pages
...logarithms, laid down, in the first part of this article, x— a;'= log. y_ log.-= log. y — log. y1. y' Hence the logarithm of a fraction, or of the quotient...the logarithm of the numerator minus the logarithm «f the denominator. And if each member of the common equation ax=y be raised to the fractional power... | |
 | 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...logarithm of the 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... | |
 | 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 -... | |
 | John Bonnycastle - Algebra - 1829 - 372 pages
...logarithms, laid down in the first part of this article, x — a:'=log.=7, or log.^=log. y — log. 3,'. Hence the logarithm of a fraction, or of the quotient...logarithm of the denominator. And if each member of the common equation a*—-y !je raised to the fractional power denoted by — , we shall have, mm m that... | |
 | 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... | |
 | John Bonnycastle - Algebra - 1834 - 330 pages
...logarithms laid y y down in the first part of this article, x— x?=\og. -„ or log. ^,=iog. i/ -log. y1. Hence the logarithm of a fraction, or of the quotient...arising from dividing one number by another, is equal tothe logarithm of the numerator minus the logarithm of the denominator. And if each member of the... | |
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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... 
