 | Benjamin Peirce - Algebra - 1855 - 308 pages
...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, diminished by the logarithm of the divisor. 14. Corollary. We have, by arts. 13 and 9, log. — = log. 1 — log. n = — log. n ; that is, the... | |
 | Charles Davies - Navigation - 1857 - 452 pages
...Dividing equation (1) by equation (2), member by member, we have, MM 10 =д^ог, m — n = log -y: hence, The logarithm of the quotient of two numbers,...of any number by 10, will be greater by 1 than the logarithm of that number ; also, Ле logaritJim of the quotient of any number divided by 10, will... | |
 | Adrien Marie Legendre, Charles Davies - Geometry - 1857 - 442 pages
...equation (1) by equation (2), member by member, we have, , , Jf J/ 10m~" = .^or, m — n = log.r^: hence, The logarithm of the quotient of two numbers,...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 by 1 than the logarithm of that... | |
 | Henry William Jeans - 1858 - 106 pages
...in the 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 - 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,... | |
 | James B. Dodd - Algebra - 1859 - 368 pages
...have y=nm (41), in which x-\-y is the logarithm of the product n m. Logarithm of a Quotient. (309.) The logarithm of the quotient of two numbers, is equal to the logarithm of the dividend minus the logarithm of the divisor. Dividing the Equation ax = n by the Equation av=m, we have az-v=n-^m... | |
 | 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... | |
 | Joseph Allen Galbraith, Samuel Haughton - Logarithms - 1860 - 310 pages
...= a'» By multiplication, NX M = a»*" therefore, log NX M = n + m = log N+ log M. PROPOSITION II. The logarithm of the quotient of two numbers is equal to the difference of the logarithms of the numbers. By diviaion. N — = a"~m M therefore N log — = n —... | |
 | Joseph Allen Galbraith - 1860 - 288 pages
...By multiplication, ДГхЛГ =оnim therefore, log NX M = я + m = log N + log M. PROPoSITION II. The logarithm of the quotient of two numbers is equal to the difference of the logarithms of the numbers. By division. N — = an~m M therefore N log — = n -... | |
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The logarithm of . the quotient of two numbers, is equal to the logarithm of the dividend diminished by the logarithm of the divisor. 
