 | Isaac Dalby - Mathematics - 1806 - 526 pages
...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)... | |
 | Encyclopedias and dictionaries - 1816 - 746 pages
...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... | |
 | Bézout - Arithmetic - 1825 - 258 pages
...logarithms of two numbers is equal to the logarithm of their product, number 227. 92. The logarithm of any power of a number is equal to the logarithm of that number, multiplied by the index of the power, number 228. 93. The logarithm of the root of a number... | |
 | Thomas Curtis (of Grove house sch, Islington) - 412 pages
...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... | |
 | 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... | |
 | Silas Totten - Algebra - 1836 - 332 pages
...have, by supposing the logarithms of both members known, Ib* = Ic It has been shown, that the logarithm of any power of a number, is equal to the logarithm of the number itself, multiplied by the exponent of the power (111); hence, Ib* = xI.b, and therefore we have, x... | |
 | Benjamin Peirce - Algebra - 1837 - 300 pages
...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...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
...-|- &.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...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
...= - or e"' = -; 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
...-|- log. m -j- log. 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... | |
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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. 
