 | Benjamin Peirce - 1837 - 302 σελίδες
...-\- log. m -|- &.c. 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... | |
 | John Hymers - 1841 - 244 σελίδες
...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",... | |
 | William Chauvenet - 1843 - 102 σελίδες
...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 a'°s-*''=5'', whence the equation... | |
 | Elias Loomis - 1846 - 380 σελίδες
...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. 64 = log. 16 = 4a;, log. 128... | |
 | Elias Loomis - 1846 - 376 σελίδες
...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 means of logarithms. The... | |
 | J. Goodall, W. Hammond - 1848 - 390 σελίδες
...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... | |
 | William Smyth - 1851 - 272 σελίδες
...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,... | |
 | Elias Loomis - 1855 - 192 σελίδες
...-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, we have the following RULE. Multiply... | |
 | Elias Loomis - 1855 - 356 σελίδες
...have log. 20 =x+l, log. 20000 = log. 2000=a;+3, log. 2000000=, &c. We have seen, in Art. 340, that the logarithm of any power of a number is equal to the logarithm of that number multiplied bv the exponent of the power. Hence, log. 4 =2x, log. 32 = log. 16=4a;, log. 128=, &c. Hence we find,... | |
 | Benjamin Peirce - 1855 - 308 σελίδες
...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 — ran, in the... | |
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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. 
