| John Hymers - Logarithms - 1841 - 244 pages
...generally, that the logarithm of a 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. ч 102 Since m - o*, n — а", та* .-.-=— = а-', n а? •'•... | |
| Charles Davies, William Guy Peck - Mathematics - 1855 - 628 pages
...the factors, taken separately. 2. The logarithm of the quotient of one number by another, is ci/ual to the logarithm of the dividend, minus the logarithm of the divisor. 3. The logarithm of any power oj a. quantity, is equal to the product of the logarithm of the quantity... | |
| Charles Davies - Algebra - 1857 - 408 pages
...I -— 1 ; that is, The logarithm of the quotient which arises from dividing one number by another is equal to the logarithm of the dividend minus the logarithm of the divisor. 232i If we raise both members of equation (1) to the «'* power, we have, a*.' = N'n (5). But from... | |
| 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°... | |
| Isaac Todhunter - Algebra - 1858 - 528 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 of the dividend diminished by the logarithm of the divisor. For let x — log. m, y = log. n ; therefore m = a', therefore... | |
| 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. w+2M(-Li + 3-^-j. -H This last equation... | |
| Charles Davies - Algebra - 1860 - 412 pages
...definition, j that is, The logarithm of the quotient which arises from dividing on' number by another is equal to the logarithm of the dividend minus the logarithm of the divisor. 232i If we raise both members of equation (1) to the n'* power, we have, a«' = N'a ..... (5). But... | |
| Charles Davies - Algebra - 1860 - 412 pages
...(N' \ -]yr)-> that is, The logarithm of the quotient which arises from dividing one number by another is equal to the logarithm of the dividend minus the logarithm of tin divisor. 232t If we raise both members of equation (1) to the nth power, we have, But from the... | |
| 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... | |
| Benjamin Greenleaf - Geometry - 1862 - 518 pages
...Multiplying equations, member by member, we have Therefore, log (MX N) =. x -\-y = log M+ log N. 10. The logarithm of a QUOTIENT is equal to the logarithm of the dividend diminished by tftat of the divisor. For, by Art. 9, we have M=a*, N=a". * Dividing the first equation... | |
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