| Benjamin Peirce - Algebra - 1855 - 308 pages
...product diminished by the logarithm of the other factor ; or, in other words, The logarithm «ft/ie quotient is equal to the logarithm of the dividend,...13 and 9, log. — = log. 1 — log. n = — log. n ; that is, the logarithm of the reciprocal of a number is the negative of the logaiithm of the number.... | |
| Adrien Marie Legendre, Charles Davies - Geometry - 1857 - 442 pages
...have, , , Jf J/ 10m~" = .^or, m — n = 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, tf'e logarithm of the product of any number by 10, will be greater... | |
| Benedict Sestini - Algebra - 1857 - 258 pages
...same equations, we have — = -, 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... | |
| Isaac Todhunter - Algebra - 1858 - 530 pages
...therefore m/n - aa* = a'+'; therefore log, mn - x + y = log. m + log„ n. 53G. The logarithm of a quotient is equal to the logarithm of the dividend diminished by the logarithm of the divisor. For let x — log. m, y = log. n ; therefore m = a', therefore — = — = a"~' : na? therefore log,... | |
| Henry William Jeans - 1858 - 106 pages
...product: thus, if x=ab, then log. a;=log. a+log. b (6) 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=aib, or -, then о log. a;=log. a — log. b If a;=-=-, then ae log. a;=log. a+log. 6+log.... | |
| Isaac Todhunter - 1860 - 620 pages
...therefore, mn = a* a" = a" *s ; therefore, log. mn = x+y= log. m + log. n. 536. The logarithm of a quotient is equal to the logarithm of the dividend diminished by the logarithm of t/ie divisor. For let x = log. m, y = log. n ; therefore, m = a*, n = a" ; therefore, -=^ = a'-»;... | |
| Horatio Nelson Robinson - Geometry - 1860 - 470 pages
...quotient arising from the division of am by <*", is equal to ani~". Hence, the logarithm of a quotient is the logarithm of the. dividend diminished by the logarithm of the divisor. If it is required to raise a number denoted by as, to the fifth power, we write a, giving it ar» exponent... | |
| Horatio Nelson Robinson - Algebra - 1863 - 432 pages
...multiplication we have mn = a**"* ; therefore, log. mn — x-\-z = log. »»-(-log. n. 4. — The logarithm of a quotient is equal to the logarithm of the dividend diminished by the logarithm of the divisor. For, let «1 = 0", n = a* ; then x = log. то, z = log. m. By division we have _ _ a*-* • n therefore,... | |
| Olinthus Gregory - 1863 - 482 pages
...For, let— =Q, and consequently A=BxQ: we shall then have B AA=A B+AQ ; whence AQ=AA — A B. So that the 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... | |
| Benjamin Peirce - Algebra - 1864 - 298 pages
...divided by the exponent of the root. 13. Corollary. The equation log. 7w m! = log. m + log. m', g1ves log. m' = log. m m' — log. m ; that is, the logarithm...Since zero is the reciprocal of. infinity, we have uI log. 0 = — log. oo = — oo ; that is, the logarithm of xero is negative inf1nity. 16. Corollary.... | |
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