 | Charles Davies - Geometry - 1854 - 436 pages
...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 of the product of any number by 10, will be greater... | |
 | 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, 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... | |
 | 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... | |
 | Isaac Todhunter - Algebra - 1858 - 530 pages
...therefore m= a", n = d?; 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...dividend diminished by the logarithm of the divisor. For let x — log. m, y = log. n ; therefore m = a', therefore — = — = a"~' : na? therefore log,... | |
 | John Hymers - Logarithms - 1858 - 324 pages
...generally, that the logarithm of any product is equal to the sum of the logarithms of its factors. 8. The logarithm of a quotient is equal to the logarithm of the dividend diminished by that of the divisor. Since m — a", n = a", m a_ i fm\ ii .'' S" (n) = X~y= g" m ~ g° n' 9. The logarithm... | |
 | 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.... | |
 | James B. Dodd - Algebra - 1859 - 368 pages
...then and, by substituting these values in the last logarithmic equation, we have, considering that the logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor, log. (»+i>- log. B=2ar(^+^^+-pL—5.+fa,. ;)or log (w+1)= log.... | |
 | Isaac Todhunter - 1860 - 620 pages
...therefore, m = a*, n = a" ; 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... | |
 | Benjamin Greenleaf - Geometry - 1862 - 532 pages
...Multiplying equations, member by member, we have Therefore, log (MX N) — x+y = log Jf+log N. 10. The logarithm of a QUOTIENT is equal to the logarithm of the dividend diminished by that of the divisor. For, by Art. 9, we have M= a", AT = a>. Dividing the first equation by the second,... | |
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The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor. 
