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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.
University Algebra: Embracing a Logical Development of the Science, with ... - Page 258
by Charles Davies - 1870

A Course of Mathematics ...: Designed for the Use of the Officers ..., Volume 2

Isaac Dalby - Mathematics - 1806 - 526 pages
...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)...

A Course of Mathematics: Designed for the Use of the Officers and ..., Volume 2

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 —...

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

Encyclopedias and dictionaries - 1816 - 746 pages
...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...

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

Bézout - Arithmetic - 1825 - 258 pages
...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...

The London encyclopaedia, or, Universal dictionary of ..., Part 1, Volume 13

...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...

A system of popular trigonometry

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...

A New Introduction to the Science of Algebra...

Silas Totten - Algebra - 1836 - 360 pages
...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,...

An Elementary Treatise on Algebra: To which are Added Exponential Equations ...

Benjamin Peirce - Algebra - 1837 - 302 pages
...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 equal to the...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....