 | John Hymers - Logarithms - 1858 - 324 pages
...where r is any number whole or fractional, positive or negative. 10. The logarithm of the root of any number is equal to the logarithm of the number divided by the index of the root. Since m = a", .: log„ (Jm) = ^ = — (log.«»). 11. Hence, if we have to multiply two numbers together,... | |
 | Charles Davies - Algebra - 1860 - 412 pages
...=(N')"= yOF - - (6). But from the definition, — = log ("^W') ; that is, The logarithm of any root of a number is equal to the logarithm of the number divided by the index of the r.oot. 234( From the principles demonstrated in the four preceding articles, we deduce the following practical... | |
 | Henry Lee Scott - History - 1861 - 674 pages
...product of the logarithm of the number by the exponent of the power ; and the logarithm of any root of a number is equal to the logarithm of the number divided by the index of the root. These properties of logarithms greatly facilitate arithmetical operations. For if multiplication is... | |
 | Benjamin Greenleaf - Geometry - 1862 - 520 pages
...have Mm = (a*)i" = a™ . ' Therefore, log (Mn) =xm= (log M) X m. 12. The logarithm of the ROOT of any number is equal to the logarithm of the number divided by the index of the root. For, let n be any number, and take the equation (Art. 9) Therefore, log 13. Hence, by means of logarithms,... | |
 | Benjamin Greenleaf - Geometry - 1861 - 628 pages
...™ = (a*)~ = a** . Therefore, log (M m) = xm = (log M ) X m. 12. The logarithm of the ROOT of any number is equal to the logarithm of the number divided by the index of the root. For, let n be any number, and take the equation (Art. 9) 1 ,mt—\ x log Af Therefore, log WM ) = -=... | |
 | Benjamin Greenleaf - Geometry - 1863 - 504 pages
...have Mm = (a*)"1 = a™ . Therefore, log (Mm) = xm = (log M) X m. 12. The logarithm of the ROOT of any number is equal to the logarithm of the number divided by the index of the root. For, let n be any number, and take the equation (Art. 9) Therefore, log 13. Hence, by means of logarithms,... | |
 | Horatio Nelson Robinson - Algebra - 1863 - 432 pages
...have mr = a1*; therefore, log. (mr) = rx = r log. m. 6. — The logarithm of any root of a number ù equal to the logarithm of the number divided by the index of the root. For, let m = a* ; then x .— log. m. X The principal use of logarithms is to facilitate arithmetical... | |
 | Adrien Marie Legendre - Geometry - 1863 - 464 pages
...definition, * = logy^T • • • • (9.) That is, the logarithm of any root of a number is equal t& the logarithm of the number divided by the index of the root. TABLE OF LOGAEITHMS. 9. A TABLE OF LOGAEITHMS, is 'a table by means of which we can find the logarithm... | |
 | Charles William Hackley - Algebra - 1864 - 530 pages
...power. IV. Extract the пл root of both members of equation (1). ii N°=a°. x 1 .-. by definition, - is the logarithm of N"; that is to say, The logarithm...any root of a given number is equal to the logarithm oftht number divided by the index of the root. Combining the last two cases, we shall find mx whence... | |
 | Benjamin Greenleaf - Algebra - 1864 - 420 pages
...we have mr = (<f)r = a*". Therefore, log (TO') = xr = r log m. 402. The logarithm of any root of a number is equal to the logarithm of the number divided by the index of the root. For, let m = a' ; then, extracting the rth root of both members, we have 403. The arithmetical mean... | |
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The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power. 
