 | William James Milne - Algebra - 1901 - 462 pages
...Evolution by logarithms. Since logarithms are simply exponents, it follows that : 474. PRINCIPLE. — The logarithm of a root of a number is equal to the...logarithm of the number divided by the index of the required root; that is, , „,- log m lo any base, log vm = The above principle may be established... | |
 | William James Milne - Algebra - 1901 - 476 pages
...Evolution by logarithms. Since logarithms are simply exponents, it follows that : 474. PuiN'cii'LK. — Th? logarithm of a root of a number is equal to the logarithm of the »umber divided by the index of the required root; that is, n/— loe m To any base, log vm = — -... | |
 | James Harrington Boyd - Algebra - 1901 - 812 pages
...= 5 loga 21 = 5 (log. 3 + loge 7). CoaoLLAEY. — Put » = - for n in (5), then (G) log« That is, the logarithm of a root of a number is equal to the logarithm of //IK number divided by the index of the root. E. g., Loge VÏÏ9 = JY log« 119. 559. It follows from... | |
 | George Egbert Fisher - 1901 - 320 pages
...numerator is 1, this principle may be conveniently stated thus : The logarithm of a root of a number is the logarithm of the number divided by the index of the root. For, lo Eg, If logr 2401 = 4, what is log, V2401 ? We have log, д/2401 = - log, 2401 = - . 4 = 2.... | |
 | George Egbert Fisher, Isaac Joachim Schwatt - Algebra - 1901 - 664 pages
...numerator is 1, this principle may be conveniently stated thus : The logarithm of a root of a number is the logarithm of the number divided by the index of the root. For, logl (m«) = llog m = Ч Ч Eg, If log; 2401 = 4, what is log, л/2401 ? We have log?V2401 =4lo... | |
 | William James Milne - Algebra - 1902 - 620 pages
...logarithms. Since 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 - 390 pages
...Therefore by definition 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
....78542.4. 154. 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,... | |
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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. 
