| John Hymers - Logarithms - 1841 - 242 pages
...m - o*, n — а", та* .-.-=— = а-', n а? •'• 1оёа (г ) = Х - У = l°Sam - loS«n9. **The logarithm of any power of a number is equal to the** product of the logarithm of the number by the index of the power. Since m = a', .-. m' = (a')' « a",... | |
| Benjamin Peirce - Algebra - 1843 - 308 pages
...if they are all equal to each other, we have log. mmm &c. = log. m -|- log. m -j- log. m -j- &c. or **Logarithm of Root, Quotient, and Reciprocal. that...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... | |
| William Chauvenet - Binomial theorem - 1843 - 102 pages
...the dividend ; the remainder is found in the table to be the logarithm of the required quotient. 62. **The logarithm of any power of a number is equal to the logarithm of** that number multiplied by the exponent of the power. For b being any number, we have a'°g-4=6. But... | |
| Nathan Scholfield - 1845 - 896 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... | |
| 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 - Conic sections - 1845
...„•. 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... | |
| 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 definition, -... | |
| Elias Loomis - Algebra - 1846 - 380 pages
...logarithm of N", since nx is the index of that power of the base which is equal to N"; that is to say, **The logarithm of any power of a number, is equal to the logarithm of** that number multiplied ¿y the exponent of the power. EXAMPLES. Ex. 1. Find the third power of 4 by... | |
| Elias Loomis - Algebra - 1846 - 346 pages
...log. 200 = x + 2, log. 200000 = log. 2000 = x + 3, log. 2000000 =, &c. We have seen, in Art. 324, that **the logarithm of any power of a number is equal to the logarithm of** that number multiplied by the exponent of the power. Hence, log. 4 = 2a;, log. 32 = log. 8 = 3x, log.... | |
| J. Goodall, W. Hammond - 1848 - 388 pages
...subtraction is division ; multiplication is involution ; and division is the extraction of roots. 3rd. **The logarithm of any power of a number is equal to the** product of the logarithm of the number by the index of the power.—4th. The logarithm of the root... | |
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