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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 - 284 pages
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Elementary Algebra: For the Use of Schools

William Smyth - Algebra - 1851 - 272 pages
...= N, or, raising both members to the mth power, ami= Nm; whence the logarithm of Nm= mx = m log. N. That is, the logarithm of any power of a number is equal to the prodiut of the logarithm of this number by the exponent of the power. To raise a number, therefore,...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1852 - 436 pages
...10mX"=Mn, in which m X n is the logarithm of M n (Art. 1) : hence, The logarithm of any power of a given number is equal to the logarithm of the number multiplied by the exponent of the power. 16. Taking the same equation, IQ™=M, and extracting the nib. root of both members, we have m _! 10n=ifn'...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1854 - 436 pages
...WmXn=M", in which m X n is the logarithm of J/" (Art. 1) : hence, The logarithm, of any power of a given number is equal to the logarithm of the number multiplied by 'the exponent of the power. 16. Taking the same equation, 1Om = M, and extracting the nth root of both members, we have HI which...
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An Elementary Treatise on Algebra: To which are Added Exponential Ewquations ...

Benjamin Peirce - Algebra - 1855 - 308 pages
...all equal to each other, we have log. mmm &c. = log. m .\. log. m -}- log. m -j- &c. or log. mn r= n log. m ; Logarithm of Root, Quotient, and Reciprocal....the number multiplied by the exponent of the power. 12. Corollary. If we substitute p — ran, in the above equation, it becomes log. p = n log. v/ p,...
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Mathematical Key: New Combinations in Respect to the Binomial Theorem and ...

Joseph B. Mott - Algebra - 1855 - 58 pages
...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 = 4 log 3 = 4X. 477121 = 1.908484....
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A Treatise on Algebra

Elias Loomis - Algebra - 1855 - 356 pages
...have log. 20 =x+l, log. 20000 = log. 2000=a;+3, log. 2000000=, &c. We have seen, in Art. 340, that the logarithm of any power of a number is equal to the logarithm of that number multiplied bv the exponent of the power. Hence, log. 4 =2x, log. 32 = log. 16=4a;, log....
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Elements of Plane and Spherical Trigonometry: With Their Applications to ...

Elias Loomis - Trigonometry - 1855 - 192 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 have...
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Treatise on Algebra, for the Use of Schools and Colleges

William Smyth - Algebra - 1855 - 370 pages
...raising both members to the rath power, we have a^ = ym; ' whence the logarithm of ym = 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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Elements of Algebra: On the Basis of M. Bourdon, Embracing Sturm's and ...

Charles Davies - Algebra - 1857 - 408 pages
...(1) to the '* power, we have, a*.' = N'n (5). But from the definition, we have, nx' — log (N/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')~n- *JW -...
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Elements of Geometry and Trigonometry: From the Works of A.M. Legendre

Adrien Marie Legendre - Geometry - 1857 - 444 pages
...10mXn=J/n, in which m X n is the logarithm of M * (Art. 1) : hence, The logarithm of any power of a given number is equal to the logarithm of the number multiplied by the exponent of the power. 16. Taking the same equation, W'" = M, and extracting the nth root of both members, we have m _. 10"...
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