 | John Bonnycastle - 1848 - 334 pages
...PQKS = cf. af . a' . a" = a"+'+„ + „; hence log.PQBS = (2) The logarithm of a fractional quantity is equal to the logarithm of the numerator minus the logarithm of the denominator. Let a" = P and a* = Q, then x = }ogje and y = log.Q ; hence Q ~ u-- - ' .-. log,- — xy — log.P—... | |
 | John Bonnycastle - Algebra - 1851 - 288 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 a? — y be raised to the fractional power denoted by —... | |
 | Joseph Ray - Algebra - 1852 - 408 pages
...divisor, is equal to the logarithm of the quotient. The same principle may be expressed otherwise thus, the logarithm of a fraction is equal to the logarithm...numerator, minus the logarithm of the denominator. From this article, and the preceding, we see that by means of logarithms, the operation of Multiplication... | |
 | Elias Loomis - Algebra - 1855 - 356 pages
...&c. log. 160 =4a;+1, log. 16000 = log. 1600=4a;+2, log. 160000=, &c. We have seen, in Art. 339, that the logarithm of a fraction is equal to the logarithm...numerator minus the logarithm of the denominator. Hence, log. 5= log. (y) = l— a;. Hence.log. 50 =2— x, log. 5000 = log. 500 =3- x, log. 50000 =,... | |
 | Joseph B. Mott - Algebra - 1855 - 58 pages
...; aa but from equation (1), log 6 = log^ — loga; therefore, log 2 = log p — log a : a that is, the logarithm of a fraction is equal to the logarithm...numerator, minus the logarithm of the denominator. (THEOREM 2.) Or, for a more general theorem for fractions, let us resume the equation log ^ — log... | |
 | William Smyth - Algebra - 1855 - 370 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. 201. Below we have a... | |
 | Benedict Sestini - Algebra - 1857 - 258 pages
...or a*-* = - ; a* vv a" z z and consequently, x — y = I.-, that is, The logarithm of the quotient is equal to the logarithm of the numerator, minus the logarithm of the denominator. Raise to the exponent c both members of the equation a*= z, we will have (a 1 )' = z° or a" = z°,... | |
 | William Smyth - Algebra - 1858 - 344 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. 201. Below we have a... | |
 | Olinthus Gregory - 1863 - 482 pages
...logarithm of the quotient is equal to the logarithm of the dividend minus that of the divisor ; or the logarithm of a fraction is equal to the logarithm of the numerator made less by that of the denominator. 1 10. Farther, A A-" = — n A A. For A-" = — : therefore A... | |
 | Joseph Ray - Algebra - 1852 - 422 pages
...divisor, is equal to the logarithm of the quotient. The same principle may be expressed otherwise thus, the logarithm of a fraction is equal to the logarithm of the numerator minus (he logarithm of the denominator. From this article, and the preceding, we see that by means of logarithms,... | |
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... the logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator. 
