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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. "
An Elementary Treatise on Algebra: To which are Added Exponential Equations ... - Page 262
by Benjamin Peirce - 1837 - 288 pages
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A Treatise on Algebra

Benedict Sestini - Algebra - 1857 - 258 pages
...xc ; but from a"= z, we have x = lz ; hence, l.<f= cl.z; that is, The logarithm of the power of any number is equal to the logarithm of the number multiplied by the exponent. But if we take the root of the degree c of both members and consequently, lz' = - = -x; - x 1 cc now...
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An Elementary Treatise on Algebra: To which are Added Exponential Equations ...

Benjamin Peirce - Algebra - 1858 - 296 pages
...if they are all equal to each other, we have log. mmm &-c. = log. m -j- log. m -f- log. m -j- &c. or Logarithm of Root, Quotient, and Reciprocal. that...the number multiplied by the exponent of the power. 12. Corollary, If we substitute p = mn, or m = \/P, in the above equation, it becomes n log. p = n...
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A Treatise on Algebra: For the Use of Schools and Colleges

William Smyth - Algebra - 1858 - 344 pages
...raismg both members to the with power, we have a~ = 1r; whence the logarithm of y m = mx = m log y. That is, the logarithm of any power of a number is equal to the product of the logarithm of this number by the exponent of the power. To form any power whatever of...
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A Treatise on Algebra

Elias Loomis - Algebra - 1858 - 392 pages
...Nm, since mx is the exponent of that power of li.e base which is equal to Nm ; hence PROPERTY III. The logarithm of any power of a number is equal to the logu rilhm of that number multiplied by the exponent of the power. EXAMPLES. Ex. 1. Find the third...
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A Treatise on Plane and Spherical Trigonometry, and on Trigonometrical ...

John Hymers - Logarithms - 1858 - 320 pages
...diminished by that of the divisor. Since m — a", n = a", m a_ i fm\ ii .'' S" (n) = X~y= g" m ~ g n' 9. The logarithm of any power of a number is equal to the product of the logarithm of the number by the index of the power. Since m = a", .: mr = (a*)" = a",...
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Tables of Logarithms of Numbers and of Sines and Tangents for Every Ten ...

Elias Loomis - Logarithms - 1859 - 372 pages
...-0.4753 divided by -36.74. INVOLUTION BY LOGARITHMS. (14.) It is proved in Algebra, Art. 340, that the logarithm of any power of a number is equal to the logarithm of that number multiplied by the exponent of the power. Hence, to involve a number by logarithms, we,...
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An elementary Treatise on Logarithms

William Henry Johnstone - 1859 - 78 pages
...n, or x = loga m, y = loga я l ,vm ax then — = — = a'.v, n ae = \ogam-logan. 7. ln any system, the logarithm of any power of a number is equal to the logarithm of that number multiplied by the index of that power. Let a' — m, or x = loga m then m? — (a')'...
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Elements of Algebra: On the Basis of M. Bourdon, Embracing Sturm's and ...

Charles Davies - Algebra - 1860 - 414 pages
...the n'* power, we have, a' = N'a ..... (5). But from the definition, we have, nx' — log (N'*) ; that is, The logarithm of any power of a number is...the number multiplied by the exponent of the power. 233. If we extract the nth root of both members of equation {1), we shall have, a" =(N')*= \fW - -...
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University Algebra : Embracing a Logical Development of the Science with ...

Charles Davies - Algebra - 1860 - 328 pages
...members of ( 3 ) to any power denoted by p, we have, Whence, by definition, px — Log mf . . . ( ?.) That is, the logarithm of any power of a number is...logarithm of the number multiplied by the exponent of the poicer. If we extract any root of both members of ( 3 ), denoted by r, we have, a' = Whence, by definition,...
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Elements of Geometry, and Plane and Spherical Trigonometry: With Numerous ...

Horatio Nelson Robinson - Geometry - 1860 - 472 pages
...ar exponent equal to 3x5; thus, (a")i=ali, and, generally, (a")m=anm. Hence, the logarithm of the power of a number is equal to the logarithm of the number multiplied by the exponent of the power. To extract the 5th root of the number a', we write a, giving it an exponent equal to f ; thus, v/as=a?,...
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