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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. "
An Elementary Treatise on Algebra: To which are Added Exponential Equations ... - Page 262
by Benjamin Peirce - 1837 - 288 pages
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A Practical Arithmetic

George Albert Wentworth, Thomas Hill - Arithmetic - 1882 - 386 pages
...37.5. 32. log 1.05. 412. As logarithms are simply exponents, therefore (§ 381), The logarithm of a power of a number is equal to the logarithm of the number multiplied by the exponent of the power. Thus, log 57 = 7 x log 5 = 7 x 0.6990 = 4.8930. log 3" = 11 x log 3 = 11 x 0.4771 = 5.2481. 413. As...
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A Practical Arithmetic

George Albert Wentworth, Thomas Hill - Arithmetic - 1882 - 376 pages
...0.4771 = 5.2481. 413. As logarithms are simply exponents, therefore (§381), The logarithm of a root of a number is equal to the logarithm of the number multiplied by the index of the root. Thus, log 2J = | of log 2 = } X 0.3010 = 0.0753. log .002* = J of (7.3010 - 10)....
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Elementary algebra. To which is now added an appendix

James Hamblin Smith - 1883 - 468 pages
...1-7191323 their difference = -8508148 which is the logarithm of 7-092752, the quotient required. 457. The logarithm of any power of a number is equal to the product of the logarithm of the numbcr and the index denoting the power. Let m=a'. Then m'=o"; .'....
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Elements of Algebra

George Albert Wentworth - Algebra - 1897 - 536 pages
...that log — = log 1 — log m. But, since log 1 = 0, log — = — log m. III. The logarithm of a power of a number is equal to the logarithm of the number multiplied by the exponent oj the 2)owerFor, let x be the logarithm of m. Then то = ax, and mi' = (a?) P = aPx. .: log mP =...
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Elements of Plane and Spherical Trigonometry

James William Nicholson - Trigonometry - 1898 - 196 pages
...10«'-''. .•. (Art. 1), log( - )= a' — 6', or by (A), log f § ] = log a — log b. \°/ 4. lll. The logarithm of any power of a number is equal to...the number multiplied by the exponent of the power. For, Art. 2, (/)', a* = l0"'. ... (Art. 1), logai=pa', or by (A), log a" =px loga. 5. lV. The logarithm...
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Elements of Trigonometry: Plane and Spherical

Andrew Wheeler Phillips, Wendell Melville Strong - Trigonometry - 1898 - 376 pages
...dividend minus the logarithm of the divisor. Thus log»— — logam — logan. n The logarithm of the power of a number is equal to the logarithm of the number multiplied by the exponent. Thus loga m*=p loga m. To obtain the logarithm of a number to any base a from its Naperian logarithm,...
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Elements of Algebra with Exercises

George Egbert Fisher, Isaac Joachim Schwatt - Algebra - 1899 - 506 pages
...1=0. Eg, Iog2 4 = 2, and Iog2 £ = — 2. 19. Tlie logarithm of any power, integral or fractional, of a number is equal to the logarithm of the number multiplied by the exponent of the power; or, ) = p log m. Let logj m — x, then 6* = m. Raising both sides of the last equation to the pth...
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The Elements of Plane Trigonometry

Pitt Durfee - Plane trigonometry - 1900 - 120 pages
...logarithm of the divisor. Raising m = 10* to the £th power, m1ft = 10ift*, or log mk = kx = k log m. III. The logarithm of any power of a number is equal to...the number multiplied by the exponent of the power. Since a root is a fractional power, the logarithm of the kti\ root of a number is — times the logarithm...
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Secondary Algebra

George Egbert Fisher - Algebra - 1900 - 438 pages
...logj 1=0. Eg, log2 4 = 2, and log2 \ = — 2. 10. The logarithm of any power, integral or fractional, of a number is equal to the logarithm of the number multiplied by the exponent of the power ; or =/> 1og/n. Let logj m = x, then b* = m. Raising both sides of the last equation to the pth power,...
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Elements of Algebra

James Morford Taylor - Algebra - 1900 - 508 pages
...log, M — log, N. Eg , log, (243 -i- 27) = log, 243 - log, 27 = 5-3 = 2. 443. The logarithm of an;/ power of a number is equal to the logarithm of the number multiplied by the exponent of tlie, power. Proof. Let M=a'; then, for all real values of p, we have M' = a'*. § 348 Hence logt(M')=px=plogaM....
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