| Elias Loomis - Algebra - 1846 - 380 pages
...nth root of both members of equation (1), we shall obtain i 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.... | |
| Charles William Hackley - Algebra - 1846 - 503 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.... | |
| 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).... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| Benjamin Osgood Peirce - Algebra - 1855 - 288 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.... | |
| Charles Davies - Algebra - 1857 - 408 pages
...- - (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, we deduce the following practical... | |
| Adrien Marie Legendre, Charles Davies - Geometry - 1857 - 444 pages
...have, 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... | |
| |