 | Isaac Dalby - 1806 - 526 σελίδες
...explained in the Arithmetic, Art. 161, 187, thus; Since /xr*—1 = /, therefore r"~~l = -f : and because the logarithm of any power of a number is equal to...the logarithm of that number multiplied by the index or exponent denoting the power (187 Arith.) therefore (72 — l) log. r = log. -., that is, n R —... | |
 | Isaac Dalby - 1813 - 538 σελίδες
...e*I>lained in the Arithmetic, Art. 161, 187, thus: Since/" xr " " =: /, therefore r" " =^.: and because the logarithm of any power of a number is equal to the logarithm °f that number multiplied by the index or exponent denoting tiiepower(187- Arith.) therefore (n —... | |
 | 1816 - 746 σελίδες
...is the logarithm of _ a ; and fince n may be either a whole number, or a fraction, it follows, that the logarithm of any power of a number is equal to the logarithm of that number, multiplied by the exponent of the power ; alfo, that the logarithm of any root of a number is equal to the logarithm... | |
 | Thomas Curtis (of Grove house sch, Islington) - 412 σελίδες
...is the logarithm of о *; and, since n may be either a whole number or a fraction, it follows, that the logarithm of any power of a number is equal to the logarithm of that number, multiplied by the exponent of the power ; also, that the logarithm of any root of a number is equal to the logarithm... | |
 | Charles Davies - 1830 - 390 σελίδες
...a™z=nm. Here, mx is the logarithm of nm ; from which it appears, that the logarithm of the power of any number, is equal to the logarithm of that number, multiplied by the index of that power. 7. If the mth root of both members of the equation az=n, x be taken, then, a'"=nm ; but... | |
 | Robert Gibson - 1833 - 436 σελίδες
...nm. Here, mx is the logarithm of nm ; from which it appears, that the logarithm of the power of any number, is equal to the logarithm of that number, multiplied by the index of that power. 7. If the with root of both members of the equation ax=n, x- I x 1 be taken, then, am=nm;... | |
 | William Smyth - 1833 - 288 σελίδες
...both members to the mth power, we have amx — ytn whence the logarithm of yx= 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... | |
 | Silas Totten - 1836 - 360 σελίδες
...we shall have, by supposing the logarithms of both members known, 1.6* = lr It has been shown, that the logarithm of any power of a number, is equal to the logarithm of the number ilself, multiplied by the exponent of the power (111) ; hence. \.b* = x \.b, and therefore... | |
 | 1836 - 192 σελίδες
...nm. Here, mx is the logarithm of nm ; from which it appears, that the logarithm of the power of any number, is equal to the logarithm of that number, multiplied by the index of that power. 7. If the mth root of both members'of the equation ax = n, - - ix . be taken, then, am... | |
 | Benjamin Peirce - 1837 - 300 σελίδες
...= log. m -f log. m -|- log. m -|- &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 .... | |
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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. 
