 | 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... | |
 | Benjamin Peirce - Algebra - 1858 - 296 pages
...the root. 13. Corollary. The equation log. m m' = log. m -\- log. m', gives log. m' = log. m mf — log. m ; that is, -the logarithm of one factor of...dividend, diminished by the logarithm of the divisor. 14. Corollary. We have, by arts. 13 and 9, log. — = log. 1 — log. n = — log. n ; Logarithms in... | |
 | 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.... | |
 | Benjamin Peirce - Algebra - 1860 - 302 pages
...the exponent of the root. 13. Corollary. The equation log. m m' = log. m + log. m' , gives log. TO' = log. mm' — log. m; that is, the logarithm of one...dividend, diminished by the logarithm of the divisor. 14. Corollary. We have, by arts. 13 and 9, log. — = log. 1 — log. n - . Tlr = — log. n ; Logarithms... | |
 | 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... | |
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The logarithm of the quotient is equal to the logarithm of the dividend, diminished by the logarithm of the divisor. 
