| John Bonnycastle - 1813
...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 - 1824 - 516 sider
...the nature of powers, — , or a =— ,; and by the definition of logarithms, x— x'=\og. lJ ; or **log. y— log. y'— Hence the logarithm of a fraction,...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 - 1824 - 516 sider
...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 - 1825 - 312 sider
...definition of 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,...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 - 1826 - 383 sider
...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
...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 - 1830 - 264 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. 216. If in the equation... | |
| James Ryan - 1835 - 361 sider
...powers, — /, or IB— x' y a - ?-, ; and by the definition of logarithms, x— x'^log. y " • ' ; or **Hence the logarithm of a fraction, or of the quotient...numerator minus the logarithm of the denominator.** 453. And if each member of the equation, ar==y, be rais, mr m ed to the fractional power ™, we shall... | |
| Adrien Marie Legendre - 1836 - 359 sider
...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 - 1837 - 329 sider
...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... | |
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