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Books Books 21 - 30 of 192 on the log of any power of a number is equal to the logarithm of the number multiplied....  
" 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 "
Annual report of the Chief Signal Officer to the Secretary of War - Page 142
by Signal Office - 1883
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A Treatise on Algebra: Containing the Latest Improvements. Adapted to the ...

Charles William Hackley - 1849 - 504 pages
....-. 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" 1 root of both members of equation (1). ii N=u". x i .-. by definition, - is the...
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An Elementary Treatise on Algebra

Benjamin Peirce - Algebra - 1851 - 284 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...the number multiplied by the exponent of the power. or 12. Corollary. If we substitute m in the above equation, it becomes n log. p = n log. v' p, log....
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ELEMENTS OF GEOMETRY AND TRIGONOMETRY

A. M. LEGENDRE - 1852
...n , 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, i(F=M, and extracting the nib. root of both members, we have n m 1 10...
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TREATISE ON ALGEBRA.

ELIAS LOOMIS, A.M. - 1852
...is the exponent of that power of the base which is equal to N wl ; hence PROPERTY III. The logarithm of any power of a number is equal to the logarithm of that number multiplied by the exponent of the power. EXAMPLES. Ex. 1. Find the third power of 4 by...
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Elements of Geometry and Trigonometry: From the Works of A.M. Legendre ...

Charles Davies, Adrien Marie Legendre - Geometry - 1854 - 432 pages
...=M a , in which mX n is the logarithm of M" (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, W'" = M, and extracting the nth root of both members, we have m 1 10"=JIf'...
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An Elementary Treatise on Algebra: To which are Added Exponential Ewquations ...

Benjamin Peirce - Algebra - 1855 - 288 pages
...-f- log. m -j- log. m -J- &c. or Logarithm of Root, Quotient, anil Reciprocal. that is, the logarithm of any power of a number is equal to the logarithm...the number multiplied by the exponent of the power. or 12. Corollary. If we substitute m in the above equation, it becomes log. p n log. log. VP =...
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NEW COMBINATIONS Binomial Cheorem and Logorithuis;

JOSEPH B. MOTT. - 1855
...log a ; and if n = -, then log a m = - log a : mm r r 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 3 4 = 4 log 3 = 4X. 477121 1.908484....
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A Treatise on Algebra

Elias Loomis - Algebra - 1855 - 316 pages
...mx is the exponent of that power of the base which is equal to N"; hence PROPERTY III. The logarithm of any power of a number is equal to the logarithm of that number multiplied by the exponent of tfie power. EXAMPLES. Ex. 1. Find the third power of 4 by...
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A Treatise on Algebra

Benedict Sestini - 1857
...xc; but from a*= z, we have x = lz; hence, lz = cl.z; that is, The logarithm of the power of any number is equal to the logarithm of the number multiplied by the exponent. But if we take the root of the degree c of both members of the equations a* = z, we will have 5 I and...
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An Elementary Treatise on Algebra: To which are Added Exponential Equations ...

Benjamin Peirce - Algebra - 1858 - 284 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...the number multiplied by the exponent of the power. 12. Corollary. If we substitute p = m n , or in the above equation, it becomes n log. p = n log. v'...
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