 | 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 of the dividend diminished by the logarithm of the divisor. For let x — log. m, y = log. n ; therefore m = a', therefore — =... | |
 | Charles Davies - Algebra - 1859 - 324 pages
...logarithm of -д=.; hence, If one number be divided by another, the logarithm of the quotient will be equal to the logarithm of the dividend, diminished by that of the divisor. Therefore, the subtraction of logarithms corresponds to the division of their numbers. 919. Let us... | |
 | 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.... | |
 | Charles Davies - Algebra - 1861 - 322 pages
...loga rithm of -= ; hence, If one number be divided by another, the logarithm if th-« quotient will be equal to the logarithm of the dividend diminished by that of the divisor. Therefore, the subtraction of logarithms corresponds to the division of their numbers. 178. Let us... | |
 | 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, member by member,... | |
 | 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 by the second,... | |
 | Adrien Marie Legendre - Geometry - 1863 - 464 pages
...(4) by (5), member by member, we have, ~~ n ' whence, by the definition, cc — y = log I — j (7.) That is, the logarithm of a quotient is equal to the...of the divisor. 7. Raising both members of (4) to the power denoted by JP, we have, whence, by the definition, xp = log mp (8.) That is, the logarithm... | |
 | Benjamin Greenleaf - Geometry - 1863 - 502 pages
...Multiplying equations, member by member, we have Therefore, log (M X N) = x -f- y = log Jf-f log ^ 10. 7%e logarithm of a QUOTIENT is equal to the logarithm of the dividend diminished by that of the divisor. For, by Art. 9, we have Dividing the first equation by the second, member by member, we have Therefore,... | |
 | Horatio Nelson Robinson - Algebra - 1863 - 432 pages
...But by 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... | |
 | Benjamin Greenleaf - Geometry - 1863 - 504 pages
...MN= a' a" = a* + r. Therefore, log (MXN) = x +y = log M-\- log M 10. The logarithm of a QUOTIENT it equal to the logarithm of the dividend diminished by that of the divisor. For, by Art. 9, we have M=<f, N=a". Dividing the first equation by the second, member by member, we... | |
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The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor. 
