| 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 - 300 pages
...-\- log. m -\- log. m -f &c. or log. m" = » log. m ; Logarithm of Root, Quotient, and Reciprocal. **that is, the logarithm of any power of a number is...the number multiplied by the exponent of the power.** 10. Corollary. If we substitute p = *»", • m = in the above equation, it becomes log. p = n log.... | |
| Benjamin Peirce - Algebra - 1837 - 302 pages
...-f- log. m -\- 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...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.... | |
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