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 Books Books The logarithm of any POWER of a number is equal to the product of the logarithm of the number by the exponent of the power. For let m be any number, and take the equation (Art. Elements of Geometry and Trigonometry: With Practical Applications - Page 314
by Benjamin Greenleaf - 1862 - 490 pages ## A Course of Mathematics ...: Designed for the Use of the Officers ..., Volume 2

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... ## Encyclopaedia Perthensis; Or Universal Dictionary of the Arts ..., Volume 13

...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... ## A Theoretical and Practical Arithmetic: In which the Principles of that ...

Bézout - Arithmetic - 1825 - 236 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... ## The London encyclopaedia, or, Universal dictionary of ..., Part 1, Volume 13

...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... ## Elements of Algebra: Tr. from the French of M. Bourdon, for the ..., Volume 1

Bourdon (M., Louis Pierre Marie) - Algebra - 1831 - 389 pages
...both members to the power n Therefore, \ogyZ = ~. x= -. log y ; that is, the logarithm of any pmcer of a number is equal to the product of the logarithm of the number, by the exponent of the pmcer. Take n — 1, as a particular case'; there will result\ogym=m. logy, an equation which'is susceptible... ## Elements of Algebra

Bourdon (M., Louis Pierre Marie) - Algebra - 1831 - 326 pages
...whense, by raising the two members to the power -, mm — • x y* = a" Therefore, mm . = -.* = -.logy; to the product of the logarithm of the number by the exponent of the power. Let there be, as an example, n — I ; there results log ym = m . log y, an equation susceptible of... ## Elements of Algebra

William Smyth - Algebra - 1833 - 288 pages
...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 a number by means of a table... ## A New Introduction to the Science of Algebra...

Silas Totten - Algebra - 1836 - 362 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,... ## An Elementary Treatise on Algebra: To which are Added Exponential Equations ...

Benjamin Peirce - Algebra - 1837 - 302 pages
...= 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... 