Search Images Maps Play YouTube News Gmail Drive More »
Sign in
Books Books
" The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power. "
Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ... - Page 75
by Nathan Scholfield - 1845
Full view - About this book

Advanced Algebra for Colleges and Schools

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:...
Full view - About this book

The Elements of Plane and Spherical Trigonometry

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...
Full view - About this book

Mathematics, mechanics, heat

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...
Full view - About this book

School Algebra

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...
Full view - About this book

Plane Trigonometry

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,...
Full view - About this book

A College Algebra

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...
Full view - About this book

A College Algebra

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...
Full view - About this book

Plane and Spherical Trigonometry

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,...
Full view - About this book

Advanced Algebra

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...
Full view - About this book

Advanced Arithmetic

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...
Full view - About this book




  1. My library
  2. Help
  3. Advanced Book Search
  4. Download EPUB
  5. Download PDF