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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 - 276 pages
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A College Algebra

Henry Burchard Fine - Algebra - 1904 - 612 pages
...and n = a", we have m/n = a* /a" = a'i-", 738 Theorem 3. The logarithm of any power of a number is the logarithm of the number multiplied by the exponent of the power. For if m = аf, we have mr = (aT)' = a*', that is, logamr = rц = r logai. 739 Theorem 4. The logarithm...
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A College Algebra

Henry Burchard Fine - Algebra - 1904 - 616 pages
...is, lognwi/n = n — r = Iog0)u — logan. 738 Theorem 3. The logarithm, of ainj power of a number is the logarithm of the number multiplied by the exponent of the power. For if m = cf, we have mr = (aT-)r = a*r, that is, logamr = r/j. = r Iog0m. 739 Theorem 4. The logarithm...
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Plane and Spherical Trigonometry

James Morford Taylor - Trigonometry - 1905 - 256 pages
...(AT •*• N) = x — y = log, Af - loga.2v". (iii) The logarithm of any power of an arithmetic number is equal to the logarithm of the number multiplied by the exponent of the power. Let M = a*. Then, for all real values of p, we have M" = ai.*. Hence loga (Mp) = px = p loga M. (1)...
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Essentials of Algebra: Complete Course (an Adequate Preparation for the ...

John Charles Stone, James Franklin Millis - Algebra - 1905 - 792 pages
...n. J Hence, log„ = x - ;/ = log„m - logaw. (E) The logarithm of a power of a number equals the logarithm of the number, multiplied by the exponent of the power; that is, logan=p log,tn. To prove this, let ax=n. Then np = (a* )" = <#*. Hence, \oganp = px= p...
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Algebra for Secondary Schools

Webster Wells - Algebra - 1906 - 484 pages
...5. log 85|. 8. log 375. 11. log Щ . 3. log11f 6. log 175. 9. logff. 12. log 2^. 423. In any system, the logarithm of any power of a number is equal to...the number multiplied by the exponent of the power. Assume the equation a* = m\ whence, x = 1ogam. Raising both members of the assumed equation to the...
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Algebra for Secondary Schools

Webster Wells - Algebra - 1906 - 570 pages
...log 85f. 8. log 375. 11. log Щ . 3. log 11*. 6. log 175. 9. log ft. 12. Iog2tt423. In any system, the logarithm of any power of a number is equal to...the number multiplied by the exponent of the power. • Assume the equation a* = m; whence, = logam. Raising both members of the assumed equation to...
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Accounting in Theory and Practice: A Text-book for the Use of Accountants ...

George Lisle - Accounting - 1906 - 448 pages
...positive numbers is the excess of the logarithm of the dividend over the logarithm of the divisor. (3) The logarithm of any power of a number is equal to the logarithm of the number multiplied by the index of the power. If m, n, and x are any numbers, these properties may be shown thus : — (1) Multiplication...
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Elementary Algebra

George Albert Wentworth - Algebra - 1906 - 440 pages
...of a quotient is equal to the logarithm of the dividend less that of the divisor. The logarithm of a power of a number is equal to the logarithm of the number multiplied by the exponent of the power. EXERCISE 136 1. What is the logarithm of 24 if 24 = Юi-8802? 2. What is the logarithm of -fa ? 3....
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The Field Engineer: A Handy Book of Practice in the Survey, Location, and ...

William Findlay Shunk - Railroad engineering - 1908 - 388 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 number multiplied by the exponent of the power. The logarithm of any root of a number is equal to the logarithm of the number divided by the index...
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A First Course in Algebra ; A Second Course in Algebra

Webster Wells - Algebra - 1908 - 470 pages
...log-2/-. 5. Iog85f. 8. log 375. 11. log 46^3. logllJ, 6. log 175. 9. log f. 12. log 2^89. In any system, the logarithm of any power of a number is equal to...the number multiplied by the exponent of the power. Assume the equation a" = m ; whence, x = log, m. Raising both members of the assumed equation to the...
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