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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. "
Encyclopaedia Perthensis; Or Universal Dictionary of the Arts, Sciences ... - Página 323
1816
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A Treatise on Algebra

Elias Loomis - 1855 - 316 páginas
...shall obtain X therefore, according to the definition, — is the logarithm of i N"; hence PROPERTY IV. The logarithm of any root of a number is equal to the logarithm of that number divided by the index of the root. EXAMPLES. Ex. 1. Find the square root of 81 by means...
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NEW COMBINATIONS Binomial Cheorem and Logorithuis;

JOSEPH B. MOTT. - 1855
...n log a ; T —Y and if n = -, then losam = - losa : m ° m that is, the logarithm of any power or root of a number is equal to the logarithm of the number multiplied by the exponent ....... , ------ ----------- --------- (THEOREMS.) 1. log 81 = log 34 =...
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Elements of Algebra: On the Basis of M. Bourdon, Embracing Sturm's and ...

Charles Davies - 1857 - 400 páginas
...shall have, , a" -(N')~n- *JW - - (6). But from the definition, yj — — log ( n-/N') ; that is, The logarithm of any root of a number is equal to the logarithm of the number divided by the index of the root. 234i From the principles demonstrated in the four preceding • articles, we deduce...
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Elements of Geometry and Trigonometry from the Works of A. M. Legendre ...

Adrien Marie Legendre - 1857 - 448 páginas
..._. 10" =M~a' ± in which - is the logarithm of M" : that is, n The logarithm of the root of a given number is equal to the logarithm of the number divided by the index of the root. EXAMPLES. 1. What is the 5th power of 9? Log 9 = 0.954243 ; 0.954243 X 5 = 4.771215;...
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A Treatise on Plane and Spherical Trigonometry, and on Trigonometrical ...

John Hymers - 1858 - 232 páginas
...where r is any number whole or fractional, positive or negative. 10. The logarithm of the root of any number is equal to the logarithm of the number divided by the index of the root. Since m = a", .: log„ (Jm) = ^ = — (log.«»). 11. Hence, if we have to multiply...
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An elementary Treatise on Logarithms

William Henry Johnstone - 1859
...power. Let a' — m, or x = loga m ¡ then m? — (a')' or loga (m') = tx = ílogam. 8. ln any system, the logarithm of any root of a number is equal to the logarithm of that number divided by the index of that root. Let ax = m, ОГ X = loga m ; J 1 then(m)'=(a')7 or...
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Elements of Algebra: On the Basis of M. Bourdon, Embracing Sturm's and ...

Charles Davies - 1860 - 400 páginas
...equation {1), we shall have, a" =(N')*= \fW - - (6). But from the definition, — = log ("yF) ; that is, The logarithm of any root of a number is equal to the logarithm of the number divided by the index of the root. 234i From the principles demonstrated in the four preceding articles, we deduce...
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Military Dictionary

H. L. Scott - 1861
...a number is equal to the product of the logarithm of the number by the exponent of the power ; and the logarithm of any root of a number is equal to the logarithm of the number divided by the index of the root. These properties of logarithms greatly facilitate arithmetical operations. For if...
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Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - 1861 - 490 páginas
...™ = (a*)~ = a** . Therefore, log (M m) = xm = (log M ) X m. 12. The logarithm of the ROOT of any number is equal to the logarithm of the number divided by the index of the root. For, let n be any number, and take the equation (Art. 9) 1 ,mt—\ x log Af Therefore,...
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Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - 1862 - 490 páginas
...have Mm = (a*)i" = a™ . ' Therefore, log (Mn) =xm= (log M) X m. 12. The logarithm of the ROOT of any number is equal to the logarithm of the number divided by the index of the root. For, let n be any number, and take the equation (Art. 9) Therefore, log 13. Hence,...
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