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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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Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - 1869 - 516 pages
...member by member, we have Jf_ --o.-. N -* o Therefore, log I -^ I = x — y= log M — log N. 11. The logarithm of any POWER of a number is equal to the product of the logarithm of the number by the exponent of the power. For let m be any number, and take...
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A Treatise on Elementary Algebra

James Hamblin Smith - 1869 - 408 pages
...diminished by the logarithm of the divisor. Let m = a', and и = a?, Then - = a"i; n m log m - log n, 373. The logarithm of any power of a number is equal to the product of the logarithm of the number and the index denoting the power. Let m = a*. Then mr = a" =...
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An Elementary Treatise on Algebra: To which are Added Exponential Equations ...

Benjamin Peirce - Algebra - 1870 - 302 pages
...all equal to each other, we have log. mmm &c. = log. m -j- log. m -j- log. m -j- &c. or log. mn = n log. m ; Logarithm of Root, Quotient, and Reciprocal....the number multiplied by the exponent of the power. 12. Corollary. If we substitute p = m", or in the above equation, it becomes n log. p = n log. v/ p,...
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University Algebra: Embracing a Logical Development of the Science, with ...

Charles Davies - 1870 - 348 pages
...denoted by p, we have, pi p CL "~ Yfa • Whence, by definition, px — Log m? . . . ( 7.) That is, tJie logarithm of any power of a number is equal to the...the number multiplied by the exponent of the power. If we extract any root of both members of ( 3 ), denoted by r, we have, ar = Whence, by definition,...
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Elementary Algebra

James Hamblin Smith - Algebra - 1870 - 452 pages
...1-7191323 their difference = -8508148 which is the logarithm of 7'092752, the quotient required. 457. The logarithm of any power of a number is equal to the product of the logarithm of the number and the index denoting the power. Let m—ax. Then mr=arx; =r.logi....
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Elementary Trigonometry

James Hamblin Smith - Trigonometry - 1870 - 282 pages
...1-7191323 their difference = -8508148 which is the logarithm of 7-092752, the quotient required. 146. The logarithm of any power of a number is equal to the product of the logarithm of the number and the index denoting the power. Let m = a'. Then m' = a";...
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Elements of Surveying and Leveling; with Descriptions of the Instruments ...

Charles Davies - 1871 - 458 pages
...(4), to a power denoted by t, we have, l0* = m'; whence, by the definition, pt = log m, ....... (8.) That is, the logarithm of any power of a number, is...logarithm of the number multiplied by the exponent of Ike power. 8. Extracting the root, indicated by r, of both members of (4), we have, 1CT = ym; whence,...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Geometry - 1871 - 302 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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Elements of Algebra: On the Basis of M. Bourdon, Embracing Sturm's and ...

Charles Davies - Algebra - 1871 - 404 pages
...the nih power, we have, a*' = N/n ..... (5). But from the definition, we have, nxf = log (N') ; that is, The logarithm of any power of a number is equal to tht logarithm of the number multiplied by the exponent of the power. 233. If we extract the nth root...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1872 - 464 pages
...denoted by p, we have, = m r whence, by the definition, xp = log m r ..... (8.) That is, the loga/ithm of any power of a number is equal to the logarithm...the number multiplied by the exponent of the power. 8. Extracting the root, indicated by r, of both members of ( 4 ), we have, • d' = \/m ; whence,...
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