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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 Algebra: On the Basis of M. Bourdon, Embracing Sturm's and ...

Charles Davies - Algebra - 1860 - 412 pages
...members of equation (1) to the nth power, we have, But from the definition, we have, nx' = log (N'") ; that is, The logarithm of any power of a number is equal to t)ie logarithm of the number multiplied by the exponent of the power. 233. If we extract the '* root...
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Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 520 pages
...second, member by member, we have ;*- N a" Therefore, log f -^ \ =x — y = log M — log 2f. 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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Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 514 pages
...have M a' _ • - - _ ^- (T* — V' N — o' " Therefore, log f ~ 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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University Algebra: Embracing a Logical Development of the Science: With ...

Charles Davies - Algebra - 1863 - 334 pages
...members of ( 3 ) to any power denoted by p, we have, Whence, by definition, px = Log mf . . . (1.) That is, the logarithm of any power of a number is...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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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1863 - 464 pages
...both members of (4) to the power denoted by JP, we have, whence, by the definition, xp = log mp (8.) That is, the logarithm of any power of a number is equal to the logarithm of tJie number multiplied by the exponent of the power. 8. Extracting the root, indicated by r, of both...
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Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1863 - 506 pages
...member by member, we have =!=-* N ~ a" ~ Therefore, log (-^J = 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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New Higher Algebra: An Analytical Course Designed for High Schools ...

Benjamin Greenleaf - Algebra - 1864 - 420 pages
...equation by the second, member by member, we have Therefore, log TT = * ~~ y ~ log m — log . 401 1 The logarithm of any power of a number is equal to...the number multiplied by the exponent of the power. For, let m = ax ; then, raising both members to the rth power, we have mr = (<f)r = a*". Therefore,...
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A Treatise on Algebra

Elias Loomis - Algebra - 1864 - 386 pages
...logarithm ol Nm, since mx is the exponent of that power of the base which s equalt) Nm; hence PROPERTY III. The logarithm of any power of a number is equal to the toga rithm of that number multiplied by the exponent of the power. EXAMPLES. Ex. 1. Find the third...
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The Normal Elementary Geometry: Embracing a Brief Treatise on Mensuration ...

Edward Brooks - Geometry - 1868 - 294 pages
...second, we have, .Zv Hence, log ( — J = m — n, or, = log M — log N. 1o-=.3[ PRIN. 6. — The logarithm of any power of a number is equal to...the number multiplied by the exponent of the power. For, since 10* =M, if we raise both members to the rath power, we have, 10"- = JM* Hence, log M n =...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies, Adrien Marie Legendre - Geometry - 1869 - 472 pages
...(4) to the power denoted by p, we have, l01* = mp ; whence, by the definition, xp = log mr ..... (8.) That is, the logarithm of any power of a number is...the number multiplied by the exponent of the power. 8. Extracting the root, indicated by r, of both members of (4), we have, whence, by the definition,...
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