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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 Trigonometry, and on Trigonometrical Tables and Logarithms ...

John Hymers - Logarithms - 1841 - 242 pages
...m - o*, n — а", та* .-.-=— = а-', n а? •'• 1оёа (г ) = Х - У = lSam - loSn9. 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', .-. m' = (a')' a",...
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An Elementary Treatise on Algebra: To which are Added Exponential Equations ...

Benjamin Peirce - Algebra - 1843 - 308 pages
...if they are all equal to each other, we have log. mmm &c. = log. m -|- log. m -j- log. m -j- &c. or Logarithm of Root, Quotient, and Reciprocal. that...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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Binomial Theorem and Logarithms: For the Use of the Midshipmen at the Naval ...

William Chauvenet - Binomial theorem - 1843 - 102 pages
...the dividend ; the remainder is found in the table to be the logarithm of the required quotient. 62. The logarithm of any power of a number is equal to the logarithm of that number multiplied by the exponent of the power. For b being any number, we have a'g-4=6. But...
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Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ...

Nathan Scholfield - 1845 - 896 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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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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A Series on Elementary and Higher Geometry, Trigonometry, and Mensuration ...

Nathan Scholfield - Conic sections - 1845
...„•. 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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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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A Treatise on Algebra

Elias Loomis - Algebra - 1846 - 380 pages
...logarithm of N", since nx is the index of that power of the base which is equal to N"; that is to say, The logarithm of any power of a number, is equal to the logarithm of that number multiplied y the exponent of the power. EXAMPLES. Ex. 1. Find the third power of 4 by...
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A Treatise on Algebra

Elias Loomis - Algebra - 1846 - 346 pages
...log. 200 = x + 2, log. 200000 = log. 2000 = x + 3, log. 2000000 =, &c. We have seen, in Art. 324, 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, log. 4 = 2a;, log. 32 = log. 8 = 3x, log....
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Solutions to the questions of the general examination at Easter, 1848 ...

J. Goodall, W. Hammond - 1848 - 388 pages
...subtraction is division ; multiplication is involution ; and division is the extraction of roots. 3rd. 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.—4th. The logarithm of the root...
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