| Joseph Allen Galbraith - 1854
...multiplication, .2V x Ж = IOM*™; therefore, log .ZV x M = я + от = log .ЯГ+ log Ж PROPOSITION П. **The logarithm of the quotient of two numbers is equal to the** di/ennce of the logarithms of the numbers. By division, N F-»o—; therefore log — = я - m = log... | |
| Charles Davies - 1854 - 432 páginas
...Dividing equation (1) by equation (2), member 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... | |
| Adrien Marie Legendre, Charles Davies - 1857 - 432 páginas
...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, is equal to the** logarithm of the dividend diminished by the logarithm of the divisor. 5. Since the logarithm of 10... | |
| James B. Dodd - 1859 - 306 páginas
...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... | |
| Joseph Allen Galbraith, Samuel Haughton - 1860 - 252 páginas
...definition, Ar = a» M = a'» By multiplication, NX M = a»*" therefore, log NX M = n + m = log N+ **log M. PROPOSITION II. The logarithm of the quotient...the difference of the logarithms of the numbers. By** diviaion. N — = a"~m M therefore N log — = n — m = log N — log M M PROPOSITION III. The logarithm... | |
| Paul Allen Towne - 1865 - 298 páginas
...numbers, J which is 5 + 4. 13S. Again, a* = M and a" = N M By dividing we have a** = — . That is, **The logarithm of the quotient of two numbers is equal to the difference of** their logarithms, Thus, the logarithm of 100000000000 is 11. The logarithm of 100000000 is 8. And the... | |
| John Fair Stoddard, William Downs Henkle - 1866 - 528 páginas
...have aT+y—uz. PEO POSITION 5. (482.) In every system, the logarii~r.tr, of the quotient o/ t'joo **numbers is equal to the difference of the logarithms of the numbers,** since when cf—v, and a'— z wo have a*~'=-. I COR. — From these propositions we derive as a corollary... | |
| ELIAS LOOMIS, L.L.D. - 1868
...find the number corresponding to the resulting logarithm, and it will be the product required. 397. **The logarithm of the quotient of two numbers is equal to the** logarithm of the dividend diminished by that of the divisor. If we divide Eq. (1) by Eq. (2), member... | |
| Daniel Barnard Hagar - 1873 - 263 páginas
...by the other, member by member, we have ax+'=mn, in which x+y is the logarithm of the product mn. 4. **The logarithm of the quotient of two numbers is equal to the** logarithm of the dividend diminished by that of the divisor. For, dividing the equation a? = m by the... | |
| Aaron Schuyler - 1864 - 490 páginas
...75831.667. 5. Find the product of 85, .097, and .125. Ans. 1.03062. DIVISION BY LOGARITHMS. 16. Proposition. **The logarithm of the quotient of two numbers is equal to the** logarithm of the dividend minus the logarithm of the divisor. (" (1) 6-= yn; then, by def., log TO... | |
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