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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.
Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ... - Page 75
by Nathan Scholfield - 1845

Elements of Plane and Spherical Trigonometry with Logarithmic and Other ...

Simon Newcomb - Trigonometry - 1882 - 372 pages
...logarithm of the number multiplied by the exponent of the power. IV. The logarithm of the root of a number is equal to the logarithm of the number divided by the index of the root. We thus derive the following rules: To find the product of several factors by logarithms. RULE. Add...

The Franklin Elementary Algebra

Edwin Pliny Seaver, George Augustus Walton - Algebra - 1881 - 304 pages
...b", whence it appears (Art. 384) that is the logarithm of y/jV. Hence The logarithm of a root of a number is equal to the logarithm of the number divided by the index of the root. 395. Briefly expressed in formulas the propositions just proved are as follows: (1) }og(NN'N" . . .)...

The Engineer's Handy-book: Containing a Full Explanation of the Steam-engine ...

Stephen Roper - Mechanical engineering - 1884 - 740 pages
...use. Any power of a given number may be found by logarithms as follows : The logarithm of any power of a given number is equal to the logarithm of the number multiplied by the exponent of the power. Example.— To find the fifth power of 9, logarithm 9 = 0'954243...

Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...of (4), we have whence, by the definition, - = log \?m. (9.) That is, the logarithm of any root of a number is equal to the logarithm of the number divided by the. index of the root. The preceding principles enable us to abbreviate the operations of multiplication and division, by...

The Engineer's Handy-book: Containing a Full Explanation of the Steam-engine ...

Stephen Roper - Mechanical engineering - 1888 - 702 pages
...59049. Conversely. Any root of any number may be found by logarithms as follows: The logarithm of the root of a given number is equal to the logarithm of the number divided by the index of the root. Example. — To find the cube root of 4096, logarithm 4096 = 3-612360 -r- 3 = 1-204120, and the number...

The Normal Elementary Algebra: Containing the First Priniples of the Science ...

Edward Brooks - Algebra - 1888 - 344 pages
...B"XIll = AT". Whence, log Jl/" = nxm. Or log M" = nx log if. PRIN. 6. The logarithm of the root of a number is equal to the logarithm of the number divided by the index of the root. For, let m = log M. Then, . B™ = M. Taking nth root, E* = M *. Whence, logJHA=-. 71 or k if *_!**;...

College Algebra: For the Use of Academies, Colleges, and Scientific Schools ...

Edward Albert Bowser - Algebra - 1888 - 868 pages
...m" = (a1)" = a** ; whence by definition, log mp = px = p log m. (7) The logarithm of any root of a number is equal to the logarithm of the number divided by the index of the root. For let x = log m ; then m = a1. 1 1 X Therefore m? = (a*)~r = ar ; whence by definition, 1 x 1 log(m')...

A Course in Algebra: Being Course One in Mathematics in the ..., Part 1

Charles Ambrose Van Velzer, Charles Sumner Slichter - Algebra - 1888 - 234 pages
...by definition, \og,,nf=pr That is, logan>=p log,,«. (c) 10. THEOREM. The logarithm of any root of a number is equal to the logarithm of the number divided by the index of the root. Let n be any number, and let loga n—x. Then, by definition, n=a* . Consequently v/«=a?. Therefore,...