 | John Hymers - Logarithms - 1841 - 244 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", where r is any number whole or fractional,... | |
 | 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.... | |
 | William Scott - Algebra - 1844 - 568 pages
...log. x=— n log. a. Consequently, log. or"= — n log. a. Whence the logarithm of any power whatever of a number is equal to the product of the logarithm of the number by the exponent of the power. 211. Let r= \/a, and therefore r"=a. Then, by Article 210, n log. r=log. a. —...,. log. a Dividing... | |
 | Elias Loomis - Algebra - 1846 - 376 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... | |
 | Elias Loomis - Algebra - 1846 - 380 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.... | |
 | J. Goodall, W. Hammond - 1848 - 390 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 of any quantity is equal to the logarithm of the... | |
 | William Smyth - Algebra - 1851 - 272 pages
...raising both members to the mth power, ami= Nm; whence the logarithm of Nm= mx = m log. N. That is, the logarithm of any power of a number is equal to the prodiut of the logarithm of this number by the exponent of the power. To raise a number, therefore,... | |
 | William Smyth - Algebra - 1855 - 370 pages
...both members to the rath power, we have a^ = ym; ' whence the logarithm of ym = mx = m log y. That is, the logarithm of any power of a number is equal to the product of the logarithm of this number by the exponent of the power. To form any power whatever of a number by means of a table... | |
 | Elias Loomis - Trigonometry - 1855 - 192 pages
...-0.4753 divided by —36.74. INVOLUTION BY LoGARITHMS. (14.) It is proved in Algebra, Art. 340, 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, to involve a number by logarithms,... | |
 | Benjamin Peirce - Algebra - 1855 - 308 pages
...m -}- log. m -j- &c. or log. mn r= n 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. 12. Corollary. If we substitute p... | |
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The logarithm of any POWER of a number is equal to the product of the logarithm of the number by the exponent of the power. For let m be any number, and take the equation (Art. 9) M=a*, then, raising both sides to the wth power, we have Mm = (a")m = a""... 
