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Books Books 131 - 140 of 183 on the log of any power of a number is equal to the logarithm of the number multiplied....
" the log of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power. Hence, by our definition, log mf-log "
Report of the Chief Signal Officer, United States Army, to the Secretary of War - Page 142
by United States. Army. Signal Corps - 1883
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Elementary Algebra

Frederick Howland Somerville - Algebra - 1908 - 407 pages
...log m and y = log log — = log m — log n. n 1 (3) n. (Art. 438) (Art. 438) 455. The logarithm of a power of a number is equal to the logarithm of the number multiplied by the exponent of the power. Let 10* = m. (1) Raising both members of the equation to the ptb. power, 10i™ = mP. Whence, log m*>...
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Standard Algebra

William James Milne - Algebra - 1908 - 464 pages
...logarithms. Since logarithms are simply exponents, it follows that: 584. 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, log m" = n log m. For, let log„ m = x, and let n be any...
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Standard Algebra

William James Milne - Algebra - 1908 - 464 pages
...logarithms. Since logarithms are simply exponents, it follows that : 584. 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, log m" = n log m. For, let log, m = x, and let n be any...
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A Secondary Arithmetic

John Charles Stone - 1908
...Hence, log a — = x — y = logo TO — log a n. III. 77; e logarithm, of a power of a number equals the logarithm of the number, multiplied by the exponent of the power For, let a* — n. Then, nt = (a*)f = af. Hence, log a w =px =p log a w. IV. The logarithm of a root...
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A Secondary Arithmetic

John Charles Stone - 1908
...n Hence, logo ™ = x — y = logo m — log a n. III. The logarithm of a power of a number equals the logarithm of the number, multiplied by the exponent of the power For, let a 1 = n. Then, nr = (a*)' = af. Hence, Iog 0 nr=px=p logo n. IV. The logarithm of a root of...
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Plane Trigonometry

Levi Leonard Conant - Plane trigonometry - 1909 - 183 pages
...dividend minus the logarithm of the divisor. .'. log ~ — x — y — log m — log n. n 4. The logarithm of any power of a number is equal to the logarithm of the number multiplied by the index of the power. PROOF. m v = (10*)" = 10* y . .'. log m v = xy = y log m. 5. The logarithm of any...
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Practical Algebra (revised) Prepared for the Use of the Midshipmen at the ...

Stimson Joseph Brown, Paul Capron - Algebra - 1910 - 191 pages
...divisor. or Using the same quantities as in III, we have logs f —J = logs m — logo n. V. 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=b x , or logs rn = x; then m «= (5«). = 6 « or i og6 ( TO ») =nx...
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Elements of Applied Mathematics

Herbert E. Cobb - Mathematics - 1911 - 274 pages
...logarithm of the divisor. III. log 2 s = 3 log 2. 98 _ /]n0.8010\8 _ ^QO.9080 _ Q The logarithm of a power of a number is equal to the logarithm of the number multiplied by the exponent of the power. IV. log V3 = log 3* = i- log 3. V3 = 3* = (10 0 - 4771 )* = 10 0 - 2886 = 1.732. The logarithm of the...
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New High School Algebra

Webster Wells, Walter Wilson Hart - Algebra - 1912 - 424 pages
...or a rt = M f . .: logM" = px. Therefore, . log M"=plog, M. Rule. — In any system, the logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent indicating the power. EXAMPLE 1. Given log 7 = .8451, find log 7 5 . SOLUTION : log 7 5 = 5 log 7 =...
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Elements of Algebra

George Albert Wentworth - 1881 - 510 pages
...that log — = log 1 — log то. 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 exponeiti of the power. For, let z be the logarithm of m. Then m = a x , and mf - (a x )f = af*. .:...
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