 | 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 =... | |
 | 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... | |
 | Arthur Schultze - Algebra - 1905 - 674 pages
...2 ; log ] = 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... | |
 | 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... | |
 | Webster Wells - Algebra - 1906 - 550 pages
...the assumed equation to the pth powei, apx = mp; whence, loga m? =px =p loga m. 424. In any system, the logarithm of any root of a number is equal to the logarithm of the number divided by the index oj the root. For, logaVm = log.(m'-) = };log0m (§ 423). 425. Examples. 1. Given log 2 = .3010... | |
 | Arthur Schultze - Algebra - 1906 - 584 pages
...bases, we have log n*= /?log я. Eg log 2U = 10 log 2; log J = log 2-3 = -Slog 2 ; 9. The logarithm of a root of a number is equal to the logarithm of the number divided by the index. p-1 P Eg log ^7 = t log 7. Ex. 1. Given log 2 = .30103, and log 3 = .47712, find log 288. log... | |
 | Webster Wells - Algebra - 1908 - 456 pages
...the assumed equation to the pth power, ap*—иlp. whence, Iog„mp=px=j9logam. 90. In any system, the logarithm of any root of a number is equal to the logarithm of the number divided by the index of the root. — - 1 For, log„Vm = lo&,(m;)=~ logam(§ 89). 91. Examples. 1. Given log 2 =... | |
 | William Findlay Shunk - Railroad engineering - 1908 - 386 pages
...power of a number is equal to the logarithm of the number multiplied by the exponent of the power. The logarithm of any root of a number is equal to the logarithm of the number divided by the index of the root. . 6. The preceding principles enable us to abridge labor in arithmetical calculations,... | |
 | Frederick Howland Somerville - Algebra - 1908 - 428 pages
...logmf=px. But, from (1), x = log m, , (Art. 438) Hence, log m" = pQog "0 • 456. The logarithm of a root of a number is equal to the logarithm of the number divided by the index of the root. Let 10« = m. (1) Raising both members to the power indicated by -, x 1 9 10« =... | |
 | Levi Leonard Conant - Trigonometry - 1909 - 320 pages
...number multiplied by the index of the power. PROOF. m? = (10*)" = 10*». .'. log m v = xy = y log m. 5. The logarithm of any root of a number is equal to the logarithm of the number divided by the index of the root. i -?/— —® — log m yy ' X 6. The logarithm of any integral power or root of... | |
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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. 
