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" the log of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power. Hence, by our definition, log mf-log "
Report of the Chief Signal Officer, United States Army, to the Secretary of War - Page 116
by United States. Army. Signal Corps - 1883
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies, Adrien Marie Legendre - Geometry - 1869 - 470 pages
...denoted by p, we have, 10*' = m p ; whence, by the definition, xp = log m p (8.) That is, the logarithm 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, UK = whence, by the definition,...
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New Higher Algebra: An Analytical Course Designed for High Schools ...

Benjamin Greenleaf - 1869 - 408 pages
...member by member, we have Therefore, log f -^ j == a; — y = log TO — log n. 401 , 2Tfo logarithm of any power of a number is equal to the logarithm...the number multiplied by the exponent of the power. For, let m = a* ; then, raising both members to the rth power, we have m r = (a*)' = a xr . Therefore,...
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An Elementary Treatise on Algebra: To which are Added Exponential Equations ...

Benjamin Peirce - Algebra - 1870 - 302 pages
...-\- log. m -}- log. m -{- &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 Ike exponent of the power. 12. Corollary. If we substitute p — m n , or in the above equation, it...
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Elements of Algebra: On the Basis of M. Bourdon, Embracing Sturm's and ...

Charles Davies - Algebra - 1871 - 404 pages
...n,' = ff» ..... (5). But from the definition, we have, nx f = log (N /n ) ; that is, The logarithm of any power of a number is equal to the logarithm...the number multiplied by the exponent of the power. 233. If we extract the n th root of both members of equation (1), we shall have, a» =(2V r7 ) M =...
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New Higher Algebra: An Analytical Course Designed for High Schools ...

Benjamin Greenleaf - Algebra - 1871 - 412 pages
...member, we have Therefore, HL = * = <fy. na« log (^) = x ~ y == log m ~ log n ~ 401. The logarithm of any power of a number is equal to the logarithm...the number multiplied by the exponent of the power. For, let m = a* ; then, raising both members to the rth power, we have Therefore, log (m r ) = xr =...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1871 - 490 pages
...by the definition, xp = log m f ..... (8.) That is, the logarithm of any power of a number is eqiud to the logarithm of the number multiplied by the exponent of the power. 8. Extracting the root, indicated by r, of both members of (4), we have, a 10"' = whence, by the definition,...
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The Elements of Plane and Spherical Trigonometry ...

Alfred Challice Johnson - Spherical trigonometry - 1871 - 178 pages
...For, .e., N io" _ M " itf ~ N .*. x—y is the Log. of ^ Log. (TT?) = x — y = Log. N — Log. M. 3. The Log. of any power of a number is equal to the Log. of the number multiplied by the index of the power. For, since N = io* (N) r = (107 = io™ .'....
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Geometry - 1871 - 302 pages
...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 Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1872 - 464 pages
...denoted by p, we have, lO" = m r ' t whence, by the definition, xp = log m r (8.) That is, the logarithm 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, id' = whence, by the definition,...
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New Higher Algebra: An Analytical Course Designed for High Schools ...

Benjamin Greenleaf - 1873 - 420 pages
...second, member by member, we have Therefore, log (~ \ = x — y = log m — log n. 401« The logarithm of any power of a number is equal to the logarithm...the number multiplied by the exponent of the power. For, let m = a* ; then, raising both members to the rih power, we have Therefore, log (m r ) = xr =...
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