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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. "
Elementary Algebra Revised - Page 375
by Frederick Howland Somerville - 1913 - 447 pages
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A system of popular trigonometry

George Darley - 1835 - 142 pages
...numbers is equal to the difference of their logarithms, 7ART. 5. The logarithm of the power of any number is equal to the logarithm of the number multiplied by the index of the power, 8. AHT. 6. The logarithm of the root of any number is equal to the logarithm of...
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A New Introduction to the Science of Algebra ...

Silas Totten - Algebra - 1836 - 320 pages
...supposing the logarithms of both members known, 1.6* = Ie It has been shown, that the logarithm of any power of a number, is equal to the logarithm of the number itself, multiplied by the exponent of the power (111) ; hence, \.b" = x\.b, and therefore we have,...
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An Elementary Treatise on Algebra: To which are Added Exponential Equations ...

Benjamin Peirce - Algebra - 1837 - 302 pages
...or log. mn = n log. TO ; Logarithm of Root, Quotient, and Reciprocal. that is, the logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power. 10. Corollary. If we substitute m = Vp, in the above equation, it becomes log. p = n log. or , " log....
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An Elementary Treatise on Algebra: To which are Added Exponential Equations ...

Benjamin Peirce - Algebra - 1837 - 300 pages
...or log. m" = » log. m ; Logarithm of Root, Quotient, and Reciprocal. that is, the logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power. 10. Corollary. If we substitute p = *»", • m = in the above equation, it becomes log. p = n log....
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The elements of algebra

Andrew Bell (writer on mathematics.) - 1839 - 500 pages
...logarithms.1 For ax -=- a* = - or e"' = -; and hence x — ж'= l ~, У У1 У' or l?L = ly — ty (503.) ' The logarithm of a power of a number is equal to the...logarithm of the number multiplied by the exponent of the power.1 If ax = y, then а«.т = yn ; and therefore nx = lyn, or ly" = nly (504.) ' The logarithm...
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An Elementary Treatise on Algebra: To which are Added Exponential Equations ...

Benjamin Peirce - Algebra - 1843 - 308 pages
...m -j- log. m -j- &c. or Logarithm of Root, Quotient, and Reciprocal. that is, the logarithm of any power of a number is equal to the logarithm of the number multiplied by the ezponent of the power. 12. Corollary. If we substitute m — -/p, in the above equation, it becomes...
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A Series on Elementary and Higher Geometry, Trigonometry, and Mensuration ...

Nathan Scholfield - Conic sections - 1845 - 542 pages
...„•. by def. (2), nx is the logarithm of N ", that is to say, The, logarithm of any power of a given number is equal to the logarithm of the number multiplied by the exponent of the power. IV. Extract the n" root of both members of equation (1). x JL .: by def. (2), — is the logarithm...
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Higher Geometry and Trigonometry: Being the Third Part of a Series on ...

Nathan Scholfield - Conic sections - 1845 - 244 pages
....*. by def. (2), na; is the logarithm of N ", that is to say, The logarithm of any power of a given number is equal to the logarithm of the number multiplied by the exponent of the power. IV. Extract the w** root of both members of equation (1). x _ .-. by def. (2). — is the logarithm...
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Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ...

Nathan Scholfield - 1845 - 894 pages
....-. by def. (2), nx is the logarithm of N ", that is to say, The logarithm of any power of a given number is equal to the logarithm of the number multiplied by the exponent of the power. IV. Extract the »** root of both members of equation.(l). _1_ X N n= x _L .•. by def. (2). — is...
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A Treatise on Algebra: Containing the Latest Improvements. Adapted to the ...

Charles William Hackley - Algebra - 1846 - 542 pages
....•. by definition, nx is the logarithm of N" ; that is to say, The logarithm of any power of a given number is equal to the logarithm of the number multiplied by the exponent of the power. IV. Extract the »ith root of both members of equation (1). i * N~°=<z°. x 1 .-. by definition, -...
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