| 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 - History - 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 - 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... | |
| 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... | |
| 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 - 674 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... | |
| John Charles Stone, James Franklin Millis - Algebra - 1905 - 776 pages
...Then np = (a* )" = <#*». Hence, \oganp = px= p lognw. (F) T/ie logarithm of a root of a number equals the logarithm of the number, divided by the index of the root; that is, r — log,,n To prove this, let ax—n. is Then i/n=yax—ar. r — X lug.« 1 , Hence, log,,in=-... | |
| 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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