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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. "
Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ... - Page 73
by Nathan Scholfield - 1845
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High School Algebra: Advanced Course

Herbert Ellsworth Slaught, Nels Johann Lennes - Algebra - 1908 - 216 pages
...logarithm of the dividend minня the logarithm of the divisor. (b) Tlie logarithm of a root of a number is the logarithm of the number divided by the index of the root. That is log Y = log a — log b and log л/о = Y D n EXERCISES By means of logarithms approximate...
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High School Algebra: Complete Course

Herbert Ellsworth Slaught, Nels Johann Lennes - Algebra - 1908 - 520 pages
...logarithm of the dividend minus the logarithm of the divisor. (b) The logarithm of a root of a number is the logarithm of the number divided by the index of the root. That is log 2 = loga — log b and log л/о = D П EXERCISES By means of logarithms approximate the...
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Trigonometry

Arthur Graham Hall, Fred Goodrich Frink - Logarithms - 1909 - 264 pages
...a*. Hence, np = (a1)" = ap* or, log« (n'») = px = p loga n. (3) IV. The logarithm of the root of a number is equal to the logarithm of the number divided by the index of the root. For, if x = loga n, then n = ax. Extracting the <?th root of both members, we get V71 = яi, whence,...
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Plane Trigonometry

Levi Leonard Conant - Plane trigonometry - 1909 - 183 pages
...the power. PROOF. mv = (10*)" = 10*y. .'. log mv = xy = y log m. 5. The logarithm of any root of a number is equal to the logarithm of the number divided by the index of the root. x PROOF. VTO = Vl& = 10". , y, — X log m .'. logvm = - = — — . yy 6. The logarithm of any integral...
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Practical Calculations for Engineers: For the Use of Engineering Students ...

Charles E. Larard, Henry A. Golding - Engineering - 1909 - 463 pages
...the number itself multiplied by the index of the power, and also that the logarithm of the root of a number is equal to the logarithm of the number divided by the index of the root. This is the mathematical principle underlying the determination of powers and roots by means of the...
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Plane Trigonometry

Arthur Graham Hall, Fred Goodrich Frink - Plane trigonometry - 1909 - 276 pages
...ax. Hence, np = (a1)»1 = apx or, loga (n?) =px = p log« n. * (3) IV. The logarithm of the root of a number is equal to the logarithm of the number divided by the index of the root. For, if x = loga и, then n = a". Extracting the qth root of both members, we get = a«, whence, log«...
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Plane and Spherical Trigonometry

Levi Leonard Conant - Trigonometry - 1909 - 316 pages
...the power. PROOF. m? = (10*)" = 10*». .'. log m v = xy = y log m. 5. The logarithm of any root of a number is equal to the logarithm of the number divided by the index of the root. i -?/— —® — log m yy ' X 6. The logarithm of any integral power or root of 10 is an integral...
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Practical Algebra (revised) Prepared for the Use of the Midshipmen at the ...

Stimson Joseph Brown, Paul Capron - Algebra - 1910 - 212 pages
...(6•)» = J~, or logs (mn) =nx. But , x = logs m; logs m n = n- log s m. VI. T^e logarithm of a root of a number is equal to the logarithm of the number divided by the index of the root. Let m=b x , or logsm=a;; then or n * VII. The logarithm of a proper fraction is always a negative number,...
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A Text-book on Advanced Algebra and Trigonometry, with Tables

William Charles Brenke - Algebra - 1910 - 372 pages
...of the power times the. logarithm of the number.. IV. The logarithm of any root of ŕ number equals the logarithm of the number divided by the index of the root. (Rule III contains rule IV, since the power in question may be fractional.) 40. The following facts...
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Elements of Applied Mathematics

Herbert E. Cobb - Mathematics - 1911 - 298 pages
...log V3 = log 3* = J log 3. V3 = 3* = (10°-4771)* = 10°-2886 = 1.732. The logarithm of the root of a number is equal to the logarithm of the number divided by the index of the root. PROBLEMS 1. Multiply 28.34 by 3.376. log 28.34 = 1. log 3.376 = 0. Before finding the mantissas from...
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