| 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 - 410 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... | |
| 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... | |
| 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... | |
| 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 - 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... | |
| 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... | |
| 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... | |
| 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... | |
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