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" The logarithm of a power of a number is equal to the logarithm of the number multiplied by the exponent of the power. log» Np = p log "
Laws and Models: Science, Engineering, and Technology - Page 275
by Carl W. Hall - 2018 - 560 pages
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The elements of algebra

Andrew Bell (writer on mathematics.) - 1839 - 500 pages
...logarithms.1 For ax -=- a* = - or e"' = -; and hence x — ж'= l ~, У У1 У' or l?L = ly — ty (503.) ' The logarithm of a power of a number is equal to the logarithm of the number multiplied by the exponent of the power.1 If ax = y, then а«.т = yn ; and...
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The Complete Algebra: Designed for Use in Schools, Academies, and Colleges

Joseph Ficklin - Algebra - 1874 - 446 pages
...logarithm of the divisor from that of the dividend. Dividing m = a* by n = 0", 562. The logarithm of any power of a number is equal to the product of the exponent of the power and the logarithm of the number. Kaising both members of the equation m = a* to the rtA...
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A Practical Arithmetic

George Albert Wentworth, Thomas Hill - Arithmetic - 1881 - 446 pages
...16. log 7.5. 24. log 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, Iog57 = 7 x log 5= 7x0.6990...
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Elements of Algebra

George Albert Wentworth - Algebra - 1881 - 400 pages
...From this it follows 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 of the power. For, let x be the logarithm of m....
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A Practical Arithmetic

George Albert Wentworth, Thomas Hill - Arithmetic - 1882 - 376 pages
...log 7.5. 24. log 37.5. 32. log 1.05. C 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 5' = 7 X log 5 = 7 X 0.6990...
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The Franklin Elementary Algebra

Edwin Pliny Seaver, George Augustus Walton - Algebra - 1881 - 304 pages
...the m lb power, N ™ = &™* whence it appears (Art. 384) that mx is the logarithm of N m . Hence The logarithm of a power of a number is equal to the logarithm of the number multiplied by the exponent of the power. 394. To find the logarithm of a root....
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A Course in Algebra: Being Course One in Mathematics in the ..., Part 1

Charles Ambrose Van Velzer, Charles Sumner Slichter - Algebra - 1888 - 234 pages
...Therefore, by definition, , f«l 10g,, -| or, by equation (i), .<,. = log,, n— log,,,/-. 9. THEOREM. The logarithm of a power of a number is equal to the logarithm of the number multiplied by the exponent of the power. Let n be any number, and let log,,«...
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A High School Arithmetic (Wentworth & Hill's Practical Arithmetic)

George Albert Wentworth - Arithmetic - 1888 - 392 pages
...16. log 7.5. 24. log 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 5' = 7 X log 5= 7x0.6990...
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Elementary Algebra

Walter William Rouse Ball - Mathematics - 1890 - 512 pages
...divisor, and let n = a", .'. y = logan. m _ a* __ ry n a" = loga m — log(l n. 257. Logarithm of a Power. The logarithm of a power of a number is equal to the product of the index of the power and the logarithm of the number. Let m be the number, and let y be the power to...
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Academic Algebra

William James Milne - Algebra - 1901 - 476 pages
...Involution by logarithms. Since logarithms are simply exponents, it follows that: 472. PRINCIPLE. — The logarithm of a power of a number is equal to the logarithm of the number multiplied by the index of the power; that is, To any base, bg m" = n log m....
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