| William James Milne - Algebra - 1902 - 620 pages
...logarithms are simply exponents, it follows that : 482. PRINCIPLE. — The logarithm of the root of a **number is equal to the logarithm of the number divided by the index of the** required root; that is, To any base, log -v/m = ^^n The above principle may be established as follows:... | |
| Thomas Ulvan Taylor, Charles Puryear - Trigonometry - 1902 - 248 pages
...Therefore, log a w p =^a:, or, substituting for x its value, (d) The logarithm of a root of a number equals **the logarithm of the number divided by the index of the root.** Thus, Prcof. Let n be the number and r the index of the root. Then, log a Vw = log a n~ r = - log a... | |
| American School (Chicago, Ill.) - Engineering - 1903 - 392 pages
...l°ga (™p) = px Substituting for x its value, loga (»i?) = p loga m 64. The logarithm of a root of a **number is equal to the logarithm of the number divided by the index of the root.** By algebra, Therefore, by Art. 63, 65. A few examples will illustrate these principles. Given that... | |
| John Marvin Colaw - Algebra - 1903 - 444 pages
...7. 1.073. 10. .3213. 13. .03928. 5. 782. 8. .0282. 11. 5745. 14. 482. The logarithm of the root of a **number is equal to the logarithm of the number divided by the index of the root.** Thus, VI00OO = Vl04 = 10^. .-. log VlO0O0 = 4 -=- 2 = 2. In general, if log m = x and a = any root... | |
| James Morford Taylor - Plane trigonometry - 1904 - 192 pages
...px=p logalf. (1) If p = 1/r, from (1) it follows that (iv) The logarithm of any root of an arithmetic **number is equal to the logarithm of the number divided by the index of the root.** An expression is said to be adapted to logarithmic computation when it involves only products, quotients,... | |
| Henry Burchard Fine - Algebra - 1904 - 616 pages
...(aT-)r = a*r, that is, logamr = r/j. = r Iog0m. 739 Theorem 4. The logarithm of any root of a number is **the logarithm of the number divided by the index of the root.** For if m = a1*, ,_ . — Ü we have vm = Va** = о* , that is, log« V»t = p/ s = (log„m)/s. 740... | |
| Henry Burchard Fine - Algebra - 1904 - 612 pages
...(aT)' = a*', that is, logamr = rц = r loga»i. 739 Theorem 4. The logarithm of any root of a number is **the logarithm of the number divided by the index of the root.** For if m = <Р, •г- Ч— we have vm = vaм = a', that is, loga^m = ц /s = (logam)/s. 740 The practical... | |
| James Morford Taylor - Trigonometry - 1905 - 256 pages
...p loga M. (1) If p = l/r, from (1) it follows that (iv) The logarithm of any root of an arithmetic **number is equal to the logarithm of the number divided by the index of the root.** An expression is said to be adapted to logarithmic computation when it involves only products, quotients,... | |
| Arthur Schultze - Algebra - 1905 - 694 pages
...= log 2-8 = - 3 log 2 ; log ?-X-?Í = log 2 + 3 log 7 - 5 log 2 ; 9. TJie logarithm of a root of a **number is equal to the logarithm of the number divided by the index.** log л/л = log я* = - log a. (§ 8) P Eg log </l = I log 7. Ex. l. Given log 2 = .30103, and log... | |
| Elmer Adelbert Lyman - Arithmetic - 1905 - 270 pages
...equals the index of the , power times the logarithm of the number. IV. The logarithm of a root equals **the logarithm of the number divided by the index of the root.** For let 10* = n and 10» = m, then log n = x and log m = y. Therefore, since mn = lO'+o, log mn = x... | |
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