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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 Geometry and Trigonometry: From the Works of A.M. Legendre - Page 6
by Adrien Marie Legendre - 1874 - 455 pages

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

Adrien Marie Legendre, Charles Davies - Geometry - 1857 - 442 pages
...10mXn=J/n, in which m X n is the logarithm of M * (Art. 1) : hence, The logarithm of any power of a given number is equal to the logarithm of the number multiplied by the exponent of the power. 16. Taking the same equation, W'" = M, and extracting the nth root of both members, we have m _. 10"...

A Treatise on Algebra

Benedict Sestini - Algebra - 1857 - 258 pages
...xc ; but from a"= z, we have x = lz ; hence, l.<f= cl.z; that is, The logarithm of the power of any number is equal to the logarithm of the number multiplied by the exponent. But if we take the root of the degree c of both members and consequently, lz' = - = -x; - x 1 cc now...

A Treatise on Algebra: For the Use of Schools and Colleges

William Smyth - Algebra - 1858 - 344 pages
...raismg both members to the with power, we have a~ = 1r; whence the logarithm of y m = 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 Treatise on Algebra

Elias Loomis - Algebra - 1858 - 394 pages
...Nm, since mx is the exponent of that power of li.e base which is equal to Nm ; hence PROPERTY III. The logarithm of any power of a number is equal to the logu rilhm of that number multiplied by the exponent of the power. EXAMPLES. Ex. 1. Find the third...

A Treatise on Plane and Spherical Trigonometry, and on Trigonometrical ...

John Hymers - Logarithms - 1858 - 324 pages
...diminished by that of the divisor. Since m — a", n = a", m a_ i fm\ ii .'' S" (n) = X~y= g" m ~ g° n' 9. The logarithm of any power of a number is equal to the product of the logarithm of the number by the index of the power. Since m = a", .: mr = (a*)" = a",...

An elementary treatise on logarithms

William Henry Johnstone - 1859 - 80 pages
...n, or x = loga m, y = loga я l ,vm ax then — = — = a'.v, n ae = \ogam-logan. 7. ln any system, the logarithm of any power of a number is equal to the logarithm of that number multiplied by the index of that power. Let a' — m, or x = loga m ¡ then m? — (a')'...

Tables of Logarithms of Numbers and of Sines and Tangents for Every Ten ...

Elias Loomis - Logarithms - 1859 - 372 pages
...-0.4753 divided by -36.74. INVOLUTION BY LOGARITHMS. (14.) It is proved in Algebra, Art. 340, that the logarithm of any power of a number is equal to the logarithm of that number multiplied by the exponent of the power. Hence, to involve a number by logarithms, we,...

Elements of Algebra: On the Basis of M. Bourdon, Embracing Sturm's and ...

Charles Davies - Algebra - 1860 - 412 pages
...the n'* power, we have, a«' = N'a ..... (5). But from the definition, we have, nx' — log (N'*) ; that is, The logarithm of any power of a number is...the number multiplied by the exponent of the power. 233. If we extract the nth root of both members of equation {1), we shall have, a" =(N')*= \fW - -...