| Dionysius Lardner - Plane trigonometry - 1828 - 434 pages
...• • • • = B'(nB'""-', vl(nn'n" • •••) = In + M + In" •••• which shows that " the logarithm of the product of any numbers is equal to the sum of their logarithms." Again, let one of the equations be divided by another, n But also, n' That is, "... | |
| William Chauvenet - Binomial theorem - 1843 - 102 pages
...produce b. • PROPERTIES OP LOGARITHMS IN GENERAL. 60. The logarithm of the product of two or more numbers is equal to the sum of the logarithms of those numbers. For let b, c, d, &c. be any numbers, and a the base of any system of logarithms, then we have by the... | |
| James B. Dodd - Algebra - 1859 - 368 pages
...1 is the logarithm of a. Logarithm of a Product. (308.) The Logarithm of the product of two or more numbers, is equal to the sum of the logarithms of those numbers. In the equations ax=n and av=m, the exponents, x and y, are the logarithms of' n and m, for the base... | |
| Elias Loomis - Algebra - 1868 - 386 pages
...of logarithms. Properties of Logarithms in general. 396. The logarithm of the product of two or more numbers is equal to the sum of the logarithms of those numbers. Let a denote the base of the system; also, let m and n be any two numbers, and x and y their logarithms.... | |
| Edward Brooks - Geometry - 1868 - 284 pages
...the principle. Thus, the log. of .458 is 1.660865. PRIN. 4. — The logarithm of the product of two numbers is equal to the sum of the logarithms of those numbers. For, let M and'JVbe any two numbers, and m and n their logarithms ; then we shall have, according to... | |
| Elias Loomis - Algebra - 1873 - 396 pages
...of logarithms. Properties of Logarithms in general. 396. The logarithm of the product of two or more numbers is equal to the sum of the logarithms of those numbers. Let a denote the base of the system ; also, let m and n be any two numbers, and x and y their logarithms.... | |
| Daniel Barnard Hagar - Algebra - 1873 - 278 pages
...is written instead of —1, 2 instead of —2, etc. 3. The logarithm of the product of two or more numbers is equal to the sum of the logarithms of those numbers. For, let m and n be any two numbers, x and y their respective logarithms, and a the base of the system.... | |
| Elias Loomis - Conic sections - 1877 - 458 pages
...same quantity are multiplied by adding their exponents, the logarithm of the product of two or more numbers is equal to the sum of the logarithms of those numbers. Also, since powers of the same quantity are divided by subtracting their exponents, the logarithm of... | |
| Edward Brooks - Algebra - 1888 - 344 pages
...of the base of a system of logarithms ł unity. PRIN. 3. The logarithm of the product of two or more numbers is equal to the sum of the logarithms of those numbers. For, let m = log M, and n = log N. Then, £-»=Д/, £» = Ж Multiplying, £"+" = Л/хЛг. Hence... | |
| Charles Sumner Slichter - Functions - 1914 - 520 pages
...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 r + log« s Exercises... | |
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