 The logarithm of the product of two or more numbers is equal to the sum of the logarithms of the numbers. For, let m and n be two numbers, and x and y their logarithms. Then, by the definition of a logarithm, m — ax, and n = a".  Elementary Text-book of Trigonometry - Page 90by Robert Hamilton Pinkerton - 1884 - 176 pagesFull view - About this book
 | John Maximilian Dyer - Plane trigonometry - 1891 - 306 pages
...(9) log 125 = 6. (10) log 144 = 4. (11) log /7 = \. (12) log 2 = |. (13) log9 = 1-5. 105. Theorem 1. The logarithm of the product of two or more numbers is equal to the sum of the logarithms of each of the numbers. (1) Let there be two numbers m and n, and let a be the base. We have to show that... | |
 | John Bascombe Lock - Plane trigonometry - 1892 - 354 pages
...sin 64 (m) - 3-7-^ - ^-.=cotA. v ' cos 3A - cos 5A 5. Prove that the logarithm of the product of two numbers is equal to the sum of the logarithms of the numbers. 6. Prove that in any triangle ABC (i) (ii) 7. Shew how to solve a triangle when one Bide and two angles... | |
 | George Washington Hull - Algebra - 1895 - 358 pages
...write the minus sign over the characteristic; thus, log .2 = Г.30103. PROPERTIES OF LOGARITHMS. 273. The logarithm of the product of two or more numbers is equal to the sum of the logarithm,? of those numbers. Let m and n be any two numbers, and x and y their logarithms. Then, by... | |
 | Andrew Wheeler Phillips, Wendell Melville Strong - Trigonometry - 1898 - 362 pages
...which satisfies the equation, ax = 1n. This is written x = loga m. The logarithm of the product of two numbers is equal to the sum of the logarithms of the numbers. Thus loga;//я = logaw + logeя. The logarithm of the quotient of two numbers is equal to the logarithm... | |
 | William James Milne - Algebra - 1901 - 476 pages
...exponents of the powers to which a constant number is to be raised, it follows that : 464. PRINCIPLE. — The logarithm of the product of two or more numbers is equal to the sum of their logarithms; that is, To any base, log (win) = log m + log n. The above principle may be established... | |
 | William James Milne - Algebra - 1902 - 620 pages
...exponents of the powers to which a constant number is to be raised, it follows that : 472. PRINCIPLE. — The logarithm of the product of two or more numbers is equal to the sum of their logarithms; that is, To any base, log (mn) = log m + log ». The above principle may be established... | |
 | American School (Chicago, Ill.) - Engineering - 1903 - 390 pages
...evolution of numbers. Their great usefulness depends on the four following principles. 61. In any system, the logarithm of the product of two or more numbers is equal to the sum of the logarithms of the separate numbers. Assume ax = m (1) | Then ( loga m = x And a'* = n (2) J by § 56 j loga » = y Multiplying... | |
 | 1906 - 502 pages
...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... | |
 | William James Milne - Algebra - 1908 - 476 pages
...exponents of the powers to which a constant number is to be raised, it follows that : 573. PRINCIPLE. — The logarithm of the product of two or more numbers is equal to the sum of their logarithms; that is, To any base, log (mn) = log m + log n. For, let Iog0 in = x and log„ n... | |
 | William Findlay Shunk - Railroad engineering - 1908 - 386 pages
...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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