| Isaac Dalby - Mathematics - 1806 - 526 pages
...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)... | |
| Isaac Dalby - Mathematics - 1813 - 538 pages
...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 —... | |
| Encyclopedias and dictionaries - 1816 - 746 pages
...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... | |
| Bézout - Arithmetic - 1825 - 258 pages
...The sum of the 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
...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... | |
| William Smyth - Algebra - 1833 - 288 pages
...raising 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... | |
| 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 - 360 pages
...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 we have,... | |
| Benjamin Peirce - Algebra - 1837 - 302 pages
...to each other, we have log. mmm &c. = log. m -f- log. m -\- log. m -|- &.c. or log. mn = n log. TO ; **Logarithm of Root, Quotient, and Reciprocal. that...exponent of the power. 10. Corollary. If we substitute** m = Vp, in the above equation, it becomes log. p = n log. or , " log. n log. V>= -~n that is, the logarithm... | |
| 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... | |
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