 | 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... | |
 | Benjamin Peirce - Algebra - 1837 - 300 pages
...-|- &c. or II. 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», or n . m = */p, in the above equation, it becomes n log. p... | |
 | Benjamin Peirce - Algebra - 1837 - 302 pages
...= 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
...= -; 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- &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
...equation (1). x JL .: by def. (2), — is the logarithm of N » that is to say, The logarithm of any root of a given number is equal to the logarithm of the number divided by the index of the root. Combining the two last cases, we shall find, whence, — is the logarithm... | |
 | Nathan Scholfield - Conic sections - 1845 - 244 pages
...equation (1). x _ .-. by def. (2). — is the logarithm of N » that is to say, The logarithm of any root of a given number is equal to the logarithm of the number divided by the index of the root. Combining the two last cases, we shall find, 7/277 "* whence, —... | |
 | Nathan Scholfield - 1845 - 894 pages
...N n= x _L .•. by def. (2). — is the logarithm of N « that is to say, The logarithm of any root of a given number is equal to the logarithm of the number divided by the index of the root. Combining the two last cases, we shall find, •fjj T~ nk whence,... | |
 | Charles William Hackley - Algebra - 1846 - 542 pages
...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...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 definition, -... | |
 | Charles William Hackley - Algebra - 1846 - 544 pages
...equation (1) to the nth 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 tlie number multiplied by Oie exponent of the power. IV. Extract the n"1 root of both members of equation... | |
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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. 
