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" 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. 9) M=a*, then, raising both sides to the wth power, we have Mm = (a")m = a""... "
Elements of Plane and Spherical Trigonometry: With Practical Applications - Page 4
by Benjamin Greenleaf - 1862 - 490 pages
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A Treatise on Elementary Trigonometry

John Bascombe Lock - Trigonometry - 1885 - 368 pages
...is equal to the difference of the logarithms of the dividend and divisor (iii) The logarithm of the power of a number is equal to the product of the logarithm of the number by the index denoting the power. (iv) The logarithm of the root of a number is equal to the result of dividing...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...(4) to the power denoted by p, we have, 10*" = mfwhence, by the definition, xp = logm". (8.) 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. 8. Extracting the root, indicated...
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Plane Trigonometry and Tables

George Albert Wentworth - Plane trigonometry - 1885 - 96 pages
...— = a — 6 = log A — log B. В 4. The logarithm of a power of a number is found by multiplying the logarithm of the number by the exponent of the power. For, An= (10°)"= 10е". Therefore, log An = an = n log Л. 5. The logarithm of the root of a number is...
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Plane Trigonometry

George Albert Wentworth - 1887 - 206 pages
...log — = a — 6 = log ^4 — log B. 4. The logarithm of a power of a number is found by multiplying the logarithm of the number by the exponent of the power. For, An= (10«)n= 10«n. Therefore, log An = an = n log A. 5. The logarithm of the root of a number is found...
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A College Algebra

George Albert Wentworth - Algebra - 1888 - 514 pages
...logarithm of the dividend. (6) The logarithm of a power of a positive number is found by multiplying the logarithm of the number by the exponent of the power. For, N" = (oT)" = a"". (7) The logarithm of the real positive value of a root of a positive number is found...
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College Algebra: For the Use of Academies, Colleges, and Scientific Schools ...

Edward Albert Bowser - Algebra - 1888 - 868 pages
...— = x — y = log m — log n. n Thus, log *£ = log 42 — log 5 = log 2 + Iog3 + log? - Iog5. (6) The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power. For let x = log m ; then m = a*. Therefore...
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The Normal Elementary Algebra: Containing the First Priniples of the Science ...

Edward Brooks - Algebra - 1888 - 344 pages
...B*=N. Dividing, S^~jn = MiN. Hence, log ( M •*• N) = m — n. Or log(M + N)=-logAT-logN. PRIN. 5. The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power. For, let 7W=logJI/. Then, B» = M....
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The Field Engineer: A Handy Book of Practice in the Survey, Location, and ...

William Findlay Shunk - Railroad engineering - 1890 - 360 pages
...logarithm of a quotient is equal to the logarithm of the dividend diminished by that of the divisor. The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power. The logarithm of any root of a number...
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Logarithmic and Other Mathematical Tables

William Joseph Hussey - Logarithms - 1891 - 178 pages
...logarithm of a quotient is equal to the logarithm of the dividend, minus tJte logarithm of the divisor. The logarithm of any power of a number is equal to the logarithm of the number multiplied by the index of the power. The logari(hm of any root of a number...
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Elementary Trigonometry

John Maximilian Dyer - Plane trigonometry - 1891 - 306 pages
...should have fit n log. — — = log. mn - log. pq = log. m + log. n - log. p - log. q. 107. Theorem 3. The logarithm of any power of a number is equal to the logarithm of the number multiplied by the index of the power. Let m be any number, a the base ; we...
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