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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

## Elementary Algebra: For the Use of Schools

William Smyth - Algebra - 1851 - 272 pages
...= N, or, raising both members to the mth power, ami= Nm; whence the logarithm of Nm= mx = m log. N. That is, the logarithm of any power of a number is equal to the prodiut of the logarithm of this number by the exponent of the power. To raise a number, therefore,...

## Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1852 - 436 pages
...10mX"=Mn, in which m X n is the logarithm of M n (Art. 1) : hence, The logarithm of any power of a given number is equal to the logarithm of the number multiplied by the exponent of the power. 16. Taking the same equation, IQ™=M, and extracting the nib. root of both members, we have m _! 10n=ifn'...

## Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1854 - 436 pages
...WmXn=M", in which m X n is the logarithm of J/" (Art. 1) : hence, The logarithm, of any power of a given number is equal to the logarithm of the number multiplied by 'the exponent of the power. 16. Taking the same equation, 1Om = M, and extracting the nth root of both members, we have HI which...

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

Benjamin Osgood Peirce - Algebra - 1855 - 308 pages
...all equal to each other, we have log. mmm &c. = log. m .\. log. m -}- log. m -j- &c. or log. mn r= n log. m ; Logarithm of Root, Quotient, and Reciprocal....the number multiplied by the exponent of the power. 12. Corollary. If we substitute p — ran, in the above equation, it becomes log. p = n log. v/ p,...

## Mathematical Key: New Combinations in Respect to the Binomial Theorem and ...

Joseph B. Mott - Algebra - 1855 - 58 pages
...log a ; T —Y and if n = -, then losam = - losa : m ° m that is, the logarithm of any power or root of a number is equal to the logarithm of the number multiplied by the exponent ....... , ------ ----------- --------- (THEOREMS.) 1. log 81 = log 34 = 4 log 3 = 4X. 477121 = 1.908484....

## A Treatise on Algebra

Elias Loomis - Algebra - 1855 - 352 pages
...have log. 20 =x+l, log. 20000 = log. 2000=a;+3, log. 2000000=, &c. We have seen, in Art. 340, that the logarithm of any power of a number is equal to the logarithm of that number multiplied bv the exponent of the power. Hence, log. 4 =2x, log. 32 = log. 16=4a;, log....

## Elements of Plane and Spherical Trigonometry: With Their Applications to ...

Elias Loomis - Trigonometry - 1855 - 192 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...

## Treatise on Algebra, for the Use of Schools and Colleges

William Smyth - Algebra - 1855 - 370 pages
...raising both members to the rath power, we have a^ = ym; ' whence the logarithm of ym = mx = m log y. That is, the logarithm of any power of a number is equal to the product of the logarithm of this number by the exponent of the power. To form any power whatever of...