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" The logarithm of the product of two numbers is equal to the sum of the logarithms of the numbers. "
Manual of mathematical tables, by J.A. Galbraith and S. Haughton - Página viii
por Joseph Allen Galbraith - 1860
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Science Examinations ... Reports, Etc

1906
...it was not often taken. C. In TRIGONOMETRY the work was on the whole fairly good. Q. 33. Explain why the logarithm of the product of two numbers is * equal to the sum of the logarithms of the numbers. By means of logarithms given below, find the fifth root, and the fifth power of 0'69889 correct to...
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The Field Engineer: A Handy Book of Practice in the Survey, Location, and ...

William Findlay Shunk - 1908 - 345 páginas
...lies between 10 and 100; hence its logarithm lies between 1 and 2, as does the logarithm of 74. 5. The logarithm of the product of two numbers is equal to the sum of the logarithms of the numbers. The logarithm of a quotient is equal to the logarithm of the dividend diminished by that of the divisor....
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Plane Trigonometry and Tables

George Wentworth, David Eugene Smith - 1914 - 314 páginas
...log 0.0001 = 0. 48. log 10,000 - log 1000 + log 100,000 - log 100 = 4. 40. Logarithm of a Product. The logarithm of the product of two numbers is equal to the sum of the logarithms of the numbers. Let A and В be the numbers, and x and y their logarithms. Then, taking 10 as the base and remembering...
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Elementary Mathematical Analysis: A Text Book for First Year College Students

Charles Sumner Slichter - 1914 - 490 páginas
...by definition of a logarithm §132: loga nr = x + y or, by (1) loga nr = Iog0 n + loga r (3) Hence, the logarithm of the product of two numbers is equal to the sum of the logarithms of those numbers. In the same way, if log,, s =z , then: nrs = aI+"+* that is, loga nrs = loga n + logo...
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Plane and Spherical Trigonometry

George Wentworth, David Eugene Smith - 1915 - 230 páginas
...log 0.0001 = 0. 48. log 10,000 - log 1000 + log 100,000 - log 100 = 4. 40. Logarithm of a Product. The logarithm of the product of two numbers is equal to the к«т of the logaritJinis of the numbers. Let A and В be the numbers, and x and y their logarithms....
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Elementary Algebra: First[-second] Year Course, Volumen2

Florian Cajori - 1916
...N1, L-\-Li = logarithm of N • Nv Hence, the theorem, TTie logarithm of the product of two positive numbers is equal to the sum of the logarithms of the numbers. 112. The integral part of a logarithm is called its characteristic, and the decimal part is called...
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Elementary Algebra: Second Year Course

Florian Cajori - 1916
...Ni, L+L! = logarithm of N • N¡. Hence, the theorem, The logarithm of the product of two positive numbers is equal to the sum of the logarithms of the numbers. 112. The integral part of a logarithm is called its characteristic, and the decimal part is called...
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Plane and Spherical Trigonometry

George Neander Bauer, William Ellsworth Brooke - 1917 - 313 páginas
...illustrated is peculiar to the system of logarithms of which 10 is the base. 4. Laws of logarithms. (a) The logarithm of the product of two numbers is equal to the sum of the logarithms of the numbers. Given a* = m (1) or Iog0 m = x (3) a" = и (2) or loga n = y. (4) From the law of exponents ax+v =...
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ELEMENTARY FUNCTIONS AND APPLICATIONS

ARTHUR SULLIVAN GALE, CHARLES WILLIAM WATKEYS - 1920
...easily deduced from the corresponding properties of the exponential function as follows: 7. Theorem. The logarithm of the product of two numbers is equal to the sum of the logarithms of the numbers. Let p = bmj whence Iog6 p = m, and q = bn, whence log& q = n. Then pq = bmbn = bm+n. Therefore log?,...
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Mine Gases and Ventilation: Textbook for Students of Mining, Mining ...

James Thom Beard - 1920 - 433 páginas
...logarithmic sum is the desired product. In other words, the logarithm of the product of two or more numbers is equal to the sum of the logarithms of the numbers. 2. Division : To divide one number by another, subtract the logarithm of the divisor from that of the...
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