 | Charles William Hackley - Algebra - 1846 - 542 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 »ith root of both members of equation (1). i * N~°=<z°. x 1 .-. by... | |
 | 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,... | |
 | 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... | |
 | Benjamin Peirce - Algebra - 1855 - 308 pages
...the above 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... | |
 | Adrien Marie Legendre, Charles Davies - Geometry - 1857 - 442 pages
...10mXn=J/n, in which m X 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... | |
 | Benedict Sestini - Algebra - 1857 - 258 pages
...xc ; but from a"= z, we have x = lz ; hence, l.<f= 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 and consequently, lz' = - = -x; - x 1 cc now... | |
 | Charles Davies - Algebra - 1857 - 408 pages
...-(N')~n- *JW - - (6). But from the definition, yj — — log ( n-/N') ; that is, The logarithm of any root of a number is equal to the logarithm of the number divided by the index of the root. 234i From the principles demonstrated in the four preceding • articles,... | |
 | James B. Dodd - Algebra - 1859 - 368 pages
...for the base a; while x and y are the logarithms of n and m. Logarithm of a Power or Boot. , (310.) The logarithm of any power or root of a number, is equal to the exponent of the power or root X the logarithm of the numher. If any particular power or root, as the... | |
 | Charles Davies - Algebra - 1860 - 332 pages
...by p, we have, Whence, by definition, px — Log mf . . . ( ?.) That is, the logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the poicer. If we extract any root of both members of ( 3 ), denoted by r, we have, a' = Whence,... | |
 | Horatio Nelson Robinson - Geometry - 1860 - 470 pages
...exponent equal to 3x5; thus, (a")i=ali, and, generally, (a")m=anm. Hence, the logarithm of the power of a number is equal to the logarithm of the number multiplied by the exponent of the power. To extract the 5th root of the number a', we write a, giving it an exponent equal to... | |
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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. 
