...(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...

...Then ax = u and a» = v. By division _ u v ' or or loga ^— J = loga u - logo v. Thus the theroem: The logarithm of a quotient is equal to the logarithm...of the dividend diminished by the logarithm of the divisor. Exercises Using the logarithms given in preceding Exercise, find the logarithms of the following:...

...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:...

...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...

...(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:...

...any number of factors. Example. Iog10(79 x 642) = log,079 + log,0642. 114. Logarithm of a quotient. The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor. PROOF : As above, let logo« = x and logaV = y. Then ax = u, and...

...logarithms of the factors. We proceed to establish two other theorems that are no less fundamental. The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor. The proof is similar to that of the first theorem. Let N and NI...

...of logarithms, Iog0 (MN) = x + y = Iog0 M + logo N, *. and this equation proves the theorem. VIII. The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor. PROOF. Using the same notations as in the proof of VII, we find...

...bk+l, whence logs MN = k + 1 = logs M + logs N. This can readily be extended to three or more factors. 4) The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor. For, ~N = ~bl ~~ therefore logs jr = k — I = logs M - logs N....

...theorem replaces the operation of multiplication by the simpler operation of addition. II. In any system the logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor. a* = m To prove, log.= n = log„ m — li Let log0m bg0 n = x...