| Dionysius Lardner - Plane trigonometry - 1828 - 434 pages
...rule : " The logarithm of any power of a number is obtained by multiplying the logarithm of the number by the exponent of the power ; and the logarithm of any root of a number is obtained by dividing the logarithm of the number by the exponent of the root" Hence, if a power or... | |
| George Darley - 1835 - 142 pages
...numbers is equal to the difference of their logarithms, 7ART. 5. The logarithm of the power of any number is equal to the logarithm of the number multiplied by the index of the power, 8. AHT. 6. The logarithm of the root of any number is equal to the logarithm of... | |
| Silas Totten - Algebra - 1836 - 320 pages
...supposing the logarithms of both members known, 1.6* = Ie It has been shown, that the logarithm of any power of a number, is equal to the logarithm of the number itself, multiplied by the exponent of the power (111) ; hence, \.b" = x\.b, and therefore we have,... | |
| Benjamin Peirce - Algebra - 1837 - 300 pages
...or log. m" = » log. m ; Logarithm of Root, Quotient, and Reciprocal. that is, the logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power. 10. Corollary. If we substitute p = *»", • m = in the above equation, it becomes log. p = n log.... | |
| Benjamin Peirce - Algebra - 1837 - 302 pages
...or log. mn = n log. TO ; Logarithm of Root, Quotient, and Reciprocal. that is, the logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power. 10. Corollary. If we substitute m = Vp, in the above equation, it becomes log. p = n log. or , " log.... | |
| Andrew Bell (writer on mathematics.) - 1839 - 500 pages
...= - or e"' = -; and hence x — ж'= l ~, У У1 У' or l?L = ly — ty (503.) ' The logarithm of a power of a number is equal to the logarithm of the number multiplied by the exponent of the power.1 If ax = y, then а«.т = yn ; and therefore nx = lyn, or ly" = nly (504.) ' The logarithm... | |
| Benjamin Peirce - Algebra - 1843 - 308 pages
...m -j- log. m -j- &c. or Logarithm of Root, Quotient, and Reciprocal. that is, the logarithm of any power of a number is equal to the logarithm of the number multiplied by the ezponent of the power. 12. Corollary. If we substitute m — -/p, in the above equation, it becomes... | |
| Nathan Scholfield - Conic sections - 1845 - 542 pages
...„•. by def. (2), 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" root of both members of equation (1). x JL .: by def. (2), — is the logarithm... | |
| Nathan Scholfield - Conic sections - 1845 - 244 pages
....*. by def. (2), na; 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 w** root of both members of equation (1). x _ .-. by def. (2). — is the logarithm... | |
| Nathan Scholfield - 1845 - 894 pages
....-. by def. (2), 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 »** root of both members of equation.(l). _1_ X N n= x _L .•. by def. (2). — is... | |
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