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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. "
The Field Engineer: A Handy Book of Practice in the Survey, Location, and ... - Página 4
por William Findlay Shunk - 1880 - 318 páginas
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High School Algebra: Complete Course

Herbert Ellsworth Slaught, Nels Johann Lennes - 1908 - 494 páginas
...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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Plane Trigonometry

Levi Leonard Conant - 1909 - 183 páginas
...number multiplied by the index of 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...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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Plane and Spherical Trigonometry

Levi Leonard Conant - 1909 - 222 páginas
...number multiplied by the index of 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...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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Trigonometry

Arthur Graham Hall, Fred Goodrich Frink - 1909 - 239 páginas
...then n = 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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Practical Algebra (revised) Prepared for the Use of the Midshipmen at the ...

Stimson Joseph Brown, Paul Capron - 1910 - 191 páginas
...power. Let m=bx, or log6m=a;,then TOn = (bx)n = bnx, or logs mn = n- logs TO. VI. The logarithm of a root of a number is equal to the logarithm of the number divided by the index of the root. Let TO = bx, or Iog6 m = x; then or Iog6 (m^) = ]-°g^. n VII. The logarithm of a proper fraction is...
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A Text-book on Advanced Algebra and Trigonometry, with Tables

William Charles Brenke - 1910 - 343 páginas
...of the power times the. logarithm of the number.. IV. The logarithm of any root of à 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 - 1911 - 274 páginas
...IV. log V3 = log 3* = £ log 3. -v/3 = 3* = (l0 °-4771 )* = 10°- 2888 = 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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Elementary Algebra: First Course

John Charles Stone, James Franklin Millis - 1911 - 311 páginas
...Then n? = (a1)»1 = afx. Hence, Iog0 if = px=p loga n. IV. The logarithm of a root of a number equals the logarithm of the number, divided by the index of the root. That is, rr log« я lOga V« = p For, let a1 = n. X Then -Ñ/ñ = vV = a'. By use of the above principles...
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First Principles of Algebra: Advanced Course

Herbert Ellsworth Slaught, Nels Johann Lennes - 1912 - 204 páginas
...logarithm of the dividend minus the logarithm of the divisor. (Ь) The logarithm of a root of a number is the logarithm of the number divided by the index of the root. That is log - = log a — log b and log \/a = Ь п EXERCISES By means of logarithms approximate the...
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Plane and Sperical Trigonometry (with Five-place Tables): A Text-book for ...

Robert Édouard Moritz - 1913 - 520 páginas
...the quantity whose яth root is to be extracted, -is the logarithm of the resulting root; hence, n The logarithm of any root of a number is equal to...logarithm of the number divided by the index of the root to be extracted, or if p=4W, iog/» = !^r. я Thus log Viy = i log 17. 26. Logarithms of Special Values....
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