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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. "
A Series on Elementary and Higher Geometry, Trigonometry, and Mensuration ... - Page 81
by Nathan Scholfield - 1845
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Introduction to the Elementary Functions

Raymond Benedict McClenon - Functions - 1918 - 264 pages
...this law n also includes as a corollary the following : The logarithm of a root of a number equals the logarithm of the number, divided by the index of the root. 154. If we now consider the application of these laws of logarithms (taking for 'base some number >1),...
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General Mathematics, Book 1

Raleigh Schorling, William David Reeve - Mathematics - 1919 - 576 pages
...so on. This illustrates the truth of another theorem, namely, that the lo</arithm of any root of a number is equal to the logarithm of the, number divided by the index of the root. Thus, log V542 = i log 542 = MIM = -1 .3670. If the logarithm of the number is negative, the root may...
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Higher arithmetic

George Wentworth - 1919 - 266 pages
...J log 42.83 = 0.5439 = log 3.499. That is, -^42.83 = 3.499. The logarithm of a root of a number is the logarithm of the number divided by the index of the root. Exercise. Computation by Logarithms Multiply as indicated, using logarithms : 1. 26 x 35. 3. 27.6 x...
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Higher Arithmetic

George Wentworth, David Eugene Smith - Arithmetic - 1919 - 268 pages
...=1.6317, J log 42.83 = 0.5439 = log 3.499. That is, ^42.83 = 3.499. The logarithm of a root of a number is the logarithm of the number divided by the index of the root. Exercise. Computation by Logarithms Multiply as indicated, using logarithms : 1. 26 x 35. 3. 27.6 x...
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Plumbers' Handbook

Samuel Edward Dibble - Plumbing - 1922 - 648 pages
...the logarithm of the number multiplied by the exponent of the power. 4. The logarithm of a root of a number is equal to the logarithm of the number divided by the index of the root. Example.— Find !/(21-2 X 1.62)2 by iogarithmg_ log 21.2 = 1.3263 log 1.62 = 0.2095 add 1.5358 multiply...
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An Introduction to Mathematical Analysis

Frank Loxley Griffin - Calculus - 1922 - 550 pages
...times the logarithm of the number : log an = n log a (IV) The logarithm of a root of a number equals the logarithm of the number, divided by the index of the root : log ^/a = - log a. If a formal proof of these laws is desired, it can be given as in the following...
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A Second Course in Algebra, Book 2

Edward Ira Edgerton, Perry Amherst Carpenter - Algebra - 1924 - 492 pages
...power, (10*)" = 10*" = M". Hence, log M" — xn = n • log M. The logarithm of a root of a number is the logarithm of the number divided by the index of the root, or, stated ui symbols, Log VM = 1 log M. n Proof: Let x = log M, so that 10* = M. Extracting the nth...
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Junior Mathematics, Volume 3

Ernst Rudolph Breslich - Mathematics - 1926 - 272 pages
...roots by logarithms is exceedingly simple. The following theorem is used : The logarithm of a root of a number is equal to the logarithm of the number divided by the index of the root, ie, . n— log a log-ya = — ^n To prove this let log a = m. Thena = 10 m . . m .'.loga-=— n or...
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Mathematics of Finance

Lloyd Leroy Smail - Finance - 1925 - 338 pages
...number multiplied by the exponent of the power: log M" = n log M. IV. The logarithm of a root of a number is equal to the logarithm of the number divided by the index of the root: log \/M = - log M. n - ^ As an example of the detailed prtJof of these laws, let us consider the first....
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Statistics as Applied in Business

Benjamin Franklin Young - Business - 1925 - 778 pages
...log 1.43136 which is the logarithm of 27, the cube of 3. 4. Roots — The logarithm of any root of a number is equal to the logarithm of the number divided by the index of the root. Specifically, we (i) find the logarithm of the number, (2) divide it by the index of the root, and...
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