| 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
...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 the logarithm of the denominator. From this article, and the preceding, we see that by means of logarithms, the operation of Multiplication... | |
| Charles Davies - Navigation - 1852 - 412 pages
...by equation (2), member by member, we have, MM 10m n = i^or, m — n = logjr: hence, The logarithm of the quotient of two numbers, is equal to the logarithm of the dividend diminished by the logarithm of the divisor. 5. Since the logarithm of 10 is 1, the logarithm... | |
| Adrien Marie Legendre - Geometry - 1852 - 436 pages
...equation (2), member by member, we have, mn MM 10 -=_r~0r, ra — tt = log-r^: hence, The logarithm of . the quotient of two numbers, is equal to the logarithm of the dividend diminished by the logarithm of the divisor. 5. Since the logarithm of 10 is 1, the logarithm... | |
| Henry Law - Logarithms - 1853 - 84 pages
...the logarithms of m and n is the logarithm of their product. PROPOSITION N. THEOREM. The logarithm of the quotient of two numbers is equal to the logarithm of the dividend, with the logarithm of the divisor subtracted from it. Let X and / denote the same as in the... | |
| Charles Davies - Navigation - 1854 - 446 pages
...equation (1) by equation (2), member by member, we have, 10m~n = -^or, m — n~logj^: hence, The logarithm of the quotient of two numbers, is equal to the logarithm of the dividend diminished by the logarithm of the divisor. 5. Since the logarithm of 10 is 1, the logarithm... | |
| Charles Davies - Geometry - 1854 - 436 pages
...equation (1) by equation (2), member by member, we have, JO™ »BB_OTjW_Wesi0g— : hence, The logarithm of the quotient of two numbers, is equal to the logarithm of the dividend diminished by the logarithm of the divisor. 5. Since the logarithm of 10 is 1, the logarithm... | |
| Joseph B. Mott - Algebra - 1855 - 58 pages
...log 6 = log^ — loga; therefore, log 2 = log p — log a : a that is, the logarithm of a fraction is equal to the logarithm of the numerator, minus the logarithm of the denominator. (THEOREM 2.) Or, for a more general theorem for fractions, let us resume the equation log ^ — log... | |
| Elias Loomis - Algebra - 1855 - 356 pages
...hence, PROPERTY II. The logarithm of a fraction, or of the quotient of one number divided by another, is equal to the logarithm of the numerator, minus the logarithm of the denominator. Hence we see that if we wish to divide one number by another, we have only to subtract the logarithm... | |
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