| Horatio Nelson Robinson - Algebra - 1863 - 432 pages
...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 we have _ _ a*-* • n therefore,... | |
| Horatio Nelson Robinson - Algebra - 1864 - 444 pages
...have mn = a*+* ; therefore, log. mn = x-\-z = log. m-|-log. и. 4. — The logarithm of q quotient **is equal to the logarithm of the dividend diminished by the logarithm of the divisor.** For, let m = a", n •=. a* ; then x = log. m, z = log. n. By division we have _ — a»-» • я... | |
| Paul Allen Towne - Algebra - 1865 - 314 pages
...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... | |
| Isaac Todhunter - Plane trigonometry - 1866 - 206 pages
...therefore mn = a'+* ; therefore log, mn = x + y= log, m + log, n. 54. The logarithm of a, quotient **is equal to the logarithm of the dividend diminished by the logarithm of the divisor.** For let jB=log,m, and y=log.n; therefore !?? = ££=«*-»; therefore log. - =jc—y=log,m- log. n.... | |
| Charles Davies - Navigation - 1866 - 422 pages
...equation (2), member Ъу member, we have, 10m~~" = -y or, m — n — \og-y-. hence, The logarithm of (he **quotient of two numbers, is equal to the logarithm of the dividend diminished** Ъу the logarithm of the divisor. 5. Since the logarithm of 10 is 1, the logarithm of the product... | |
| Elias Loomis - Algebra - 1868 - 386 pages
...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 by member, we shall have a x -v=~. n Therefore,... | |
| James Hamblin Smith - 1869
...and n = a". Then mn = a'+s ; «'. log ти = x + y = log m + log n. 372. The logarithm of a quotient **is equal to the logarithm of the dividend diminished by the logarithm of the divisor.** Let m = a', and и = a?, Then - = a"i; n m log m - log n, 373. The logarithm of any power of a number... | |
| Isaac Todhunter - Algebra - 1870 - 608 pages
...therefore mn = a1 a" = et**; therefore loganm = x + y = logam + logaw. 536. The logarithm of a quotient **is equal to the logarithm of the dividend diminished by the logarithm of the divisor.** thereforo m = a", n = a? ; ma!° therefore — = — = a"-" ; no? therefore Iog0 - =x — y = logam... | |
| James Hamblin Smith - 1870
...treating of logarithms to the particular base 10, we may omit the suffix. 456. The logarithm of a quotient **is equal to the logarithm of the dividend diminished by the logarithm of the divisor.** Let m = a", and n=aS. Then - = o"-'; n =logant- logan. Thus the operation of Division is changed into... | |
| James Hamblin Smith - Algebra - 1870
...treating of logarithms to the particular base 10, we may omit the suffix. 456. The logarithm of a quotient **is equal to the logarithm of the dividend diminished by the logarithm of the** dicisor. Let m=a*, and n = a". Then ™ = a"-»; •• a = log(Jm-logan. Thus the operation of Division... | |
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