...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...

...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...

...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...

...(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...

...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...

...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...

...(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:...

...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...

...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:...

...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...