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" M" is the mnth power of the base b, mn is the logarithm of M". Therefore the logarithm of any power of a number is obtained by multiplying the logarithm of that number into the number denoting the power. 13. Finally, if M is a number whose logarithm is... "
Tables of Logarithms of Numbers, and of Logarithmic Sines, Tangents and ... - Pàgina 14
per Anthony Dumond Stanley - 1849 - 340 pàgines
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An Analytical Treatise on Plane and Spherical Trigonometry, and the Analysis ...

Dionysius Lardner - 1828 - 434 pàgines
...But also, nm = B'<" ', v^ Hence l(nm) = mln, lmJn— — . in Whence we have the following rule : " The logarithm of any power of a number is obtained by multiplying the logarithm of the number by the exponent of the power ; and the logarithm of any root of a number is obtained by...
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Plane trigonometry. [With] Solutions of examples

John William Colenso (bp. of Natal.) - 1851 - 148 pàgines
...evn' . & to Hence log— = logl — logm = — logwi, since logl = 0. fyi' (iii) Logm" = wlogm, or the logarithm of any power of a number is obtained by multiplying the logarithm of the number by the index of the power. For m" = (a*)" = a"*, and .-. log(»z") = nx = nlogm. As the...
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Tables of Logarithms ...: With Other Tables of Frequent Use in the Study of ...

A. D. Stanley - 1854 - 416 pàgines
...M=bm, M" = bm" ; but if M" is the mnth power of the base b, mn is the logarithm of M". Therefore ¡lie logarithm of any power of a number is obtained by...Finally, if M is a number whose logarithm is m, the log1 *« arithm of M " is — • n _L ü! For as M=bm, M"=b • Therefore the logarithm of any root...
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Textile Calculations, Manufacture and Mechanism

Joseph Henry Whitwam - 1920 - 456 pàgines
...quotient is obtained by subtracting the logarithm of the divisor from the logarithm of the dividend. III. The Logarithm of any power of a number is obtained by multiplying the logarithm of the number by the index of the power. IV. The Logarithm of any root of a number is obtained by dividing...
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