| Levi Leonard Conant - 1909 - 320 páginas
...numbers, and let x and y be their logarithms respectively. Then .'. log(ran) = x + y = log m + log n. 3. The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor. PROOF. n .-.tog 2n = log m — log n. 4. The logarithm of any power... | |
| Herbert E. Cobb - 1911 - 298 páginas
...logarithms of the factors. II. log | = log 3 -log 2. 3 -f- 2 = 10°-4m -=- 10°-801° = 10°-1761 = 1.5. The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor. III. log 2s = 3 log 2. 2» _ (100.8010)8 _ 1Q0.9080 _ g The logarithm... | |
| Edward Vermilye Huntington - 1912 - 32 páginas
...product is equal to the logarithm of the first factor plus the logarithm of the second factor; (2) The logarithm of a quotient is equal to the logarithm of the numerator minus the logarithm of the denominator; (3) The logarithm of the nth power of a number is... | |
| Frederick Howland Somerville - 1913 - 458 páginas
...(1) and (2), x = log m and y = log n. (Art. 438) Substituting in (3), log inn = logm + log n. 454. The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor. Let 10* = m (1) and 10* = n. (2) Dividing (1) by (2), |£ = ~ That... | |
| George Wentworth - 1914 - 348 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... | |
| Charles Sumner Slichter - 1914 - 520 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... | |
| Ernest Julius Wilczynski - 1914 - 296 páginas
...(2)). Therefore, by the definition of logarithms, a result which may be formulated as follows : II. The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor. The same fact may, of course, be stated in the equivalent form:... | |
| George Wentworth, David Eugene Smith - 1914 - 338 páginas
...30" = 0.5971, find 27.65 tan 30° 50' 30". 54. Division by Logarithms. It has been shown (§ 41) that the logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor. Care must be taken that the mantissa in subtraction does not become... | |
| Herbert Ellsworth Slaught - 1914 - 400 páginas
...definition of logarithms, 10go = X ~ У = 10g" M~ 10g° Д a result which may be formulated as follows : II. The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor. The same fact may, of course, be stated in the equivalent form:... | |
| National Academy of Sciences (U.S.) - 1926 - 822 páginas
...corresponding numbers in this geometric progression. From both of these definitions it results that the logarithm of the product of two numbers is equal to the sum of their logarithms, and this is usually regarded as a fundamental law of logarithms. In fact, AL Cauchy... | |
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