| Benjamin Osgood Peirce - Algebra - 1855 - 288 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 - 393 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 - Geometry - 1857 - 444 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
...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 - 496 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 - 306 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
...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 - 453 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 - 252 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
...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 -... | |
| |