 N — log. n ; from 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 of a fraction — is equal to the logarithm of its numerator minus the logarithm of its...  An elementary treatise on logarithms - Page 3by William Henry Johnstone - 1859Full view - About this book
 | 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." If... | |
 | Bewick Bridge - Algebra - 1821 - 284 pages
...the logarithm of — =x— x""=log.a* — log. of"" n = \og,N— log. я ; from 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 of a fraction Г— 1 " is equal to the logarithm of its numerator minus the... | |
 | 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 logarithm of... | |
 | 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 numerator minus the logarithm of... | |
 | George Darley - 1835 - 142 pages
...number of factors ; thus, log. (w n' n", &c.) = log. n + log. n' + log. n" +, &c. ART. 4. The log. of the quotient of any two numbers is equal to the difference of their logs. Let n, n', be any two numbers, /, I' their logs. Then log. (^)-/-f. \ n ' DEM. If r be the base,... | |
 | 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 of its numerator... | |
 | 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 the logarithms... | |
 | Bewick Bridge - Algebra - 1841 - 260 pages
...logarithm of — =x — x""=log. ax — log. a*""— 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 logarithms ; and that the logarithm of a fraction — is equal to the logarithm of its numerator minus the logarithm... | |
 | Henry W. Jeans - Trigonometry - 1842 - 138 pages
...of the logarithms of all the terms in the product : thus if x=ab then log. A =log. a + log. b. (b) The logarithm of the quotient of any two numbers is equal to the logarithm of the dividend diminished by the logarithm of the divisor : thus if x = 7 then log. x =... | |
 | Alexander Ingram - 1844 - 262 pages
...^ = r*~ * ; but the log. of r*-" = x — x, .: the log. of - = x — rf = log. a — log. b ; hence the logarithm of the quotient of any two numbers is equal to the difference of the logarithms of these numbers, or the log. of a fraction - is equal to the log. of the numerator... | |
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