| John Hymers - Logarithms - 1858 - 232 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... | |
| |