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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.
A Series on Elementary and Higher Geometry, Trigonometry, and Mensuration ... - Page 81
by Nathan Scholfield - 1845

## A Treatise on Algebra

Elias Loomis - Algebra - 1846 - 346 pages
...root of both members of equation (1), we shall obtain x 1 therefore, according to the definition, - is the logarithm of N" ; that is to say, . The logarithm of any root of a number, is equal to the logarithm of that number divided by the index of the root. EXAMPLES. Ex. 1....

## A Treatise on Algebra: Containing the Latest Improvements. Adapted to the ...

Charles William Hackley - Algebra - 1846 - 542 pages
...denominator. III. Raise both members of equation (1) to the rath power. N"=a'"t. .•. by definition, nx is the logarithm of N" ; that is to say, The logarithm of any power of a given number is equal to the logarithm of the number multiplied by the exponent of the power....

## A Treatise on Algebra: Containing the Latest Improvements. Adapted to the ...

Charles William Hackley - Algebra - 1846 - 542 pages
...power. N"=a". .-. by definition, nx is the logarithm of N° ; that is to say, The logarithm of any power of a given number is equal to the logarithm of the number multiplied by the exponent of the power. IV. Extract the n a root of both members of equation (1)....

## Elementary Algebra: For the Use of Schools

William Smyth - Algebra - 1851 - 272 pages
...am = N'n; whence log. Nm — — r= — — mm That is, the logarithm of the root of any degree of a number is equal to the logarithm of the number divided by the index of the root. The properties above are altogether independent of the base ; we may take, therefore, as we have before...

## Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1852 - 436 pages
...have, 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...

## An Introduction to Astrology

William Lilly, Zadkiel - Astrology - 1852 - 584 pages
...logarithm of the quotient. Also the logarithm multiplied by the index of the power raises the power ; and the logarithm of the number divided by the index of the root extracts the root, &c. Logarithms are a series of numbers in arithmetical progression, which answer...

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

Charles Davies - Geometry - 1854 - 436 pages
...have, 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...

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

Benjamin Osgood Peirce - Algebra - 1855 - 308 pages
...equation, it becomes log. p = n log. v/ p, log. v P = k*Z; n that is, the logarithm of any root of a number is equal to the logarithm of the number divided by the exponent of the root. 13. Corollary. • The equation log. m m' = log. TO + l°g. n»'i gives log....