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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.
Elements of Geometry and Trigonometry: From the Works of A.M. Legendre - Page 6
by Adrien Marie Legendre - 1874 - 455 pages

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...

Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 518 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...

Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 532 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...

University Algebra: Embracing a Logical Development of the Science: With ...

Charles Davies - Algebra - 1863 - 338 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,...

Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1863 - 464 pages
...Raising 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...

Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1863 - 504 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...

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,...

An Elementary Treatise on Algebra: To which are Added Exponential Equations ...

Benjamin Peirce - Algebra - 1864 - 298 pages
...&c. = log. m -\- log. m -\- log. m -f- &c, or Logarithm or Root, Quotient, and Reciprocal. that 1s, the logarithm of any power of a number is equal to...the number multiplied by the exponent of the power. 12. Corollary. If we substitute in the above equation, it becomes M log. p = n log. v/ p, log. ^p=!°gP;...