...logarithms of the several factors, we obtain the product of those factors. 5. The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor. For a " =-=V n a1a?1 .-. la (— I => la»и- \аП. \П I r log I - J = log m — log n. Hence, if...

...and x' = ly. And aх x aх = yy', or aх+х'=yy'; and hence x + x' = lyi/ or lytf = ly + ly'(502.) 1 The logarithm of the quotient of two numbers is equal to the difference of their logarithms.1 For ax -=- a* = - or e"' = -; and hence x — ж'= l ~, У У1 У'...

...them together ; the sum will be found in the table to be the logarithm of the required product. 61. The logarithm of the quotient of two numbers is equal to the difference of their logarithms. For b and c being any two numbers, we have a\og.b—l) alog.<;_cDividing...

...N' c? N .•. def. (2), x— x1 is the logarithm of that is to say, The logarithm of a fraction, or of the quotient of two numbers, is equal to the logarithm of the numerator minus the logarithm of the denominator. III. Raise both members of equation (1) to the power...

...logarithms of these factors. II. Divide equation (1) by (2), N_a* N' a* The logarithm of a fraction, or of the quotient of two numbers, is equal to the logarithm of the numerator minus the logarithm of the denominator. III. Raise both members of equation (1) to the power...

...logarithms of these factors. II. Divide equation (1) by (2), N_o*_ N'~^ The logarithm of a fraction, or of the quotient of two numbers, is equal to the logarithm of the numerator minus the logarithm of the denominator. III. Raise both members of equation (1) to the power...

....-. by definition, x — x" is the logarithm of ^ ; that is to say, The logarithm of a fraction, or of the quotient of two numbers, is equal to the logarithm of the numerator minus the logarithm of the denominator. III. Raise both members of equation (1) to the nth...

...of the expansion of HJ (« + 4 )». SECT. IV.— 1. Define the logarithm of a number, and show that the logarithm of the quotient of two numbers is equal to the difference of their logarithms. 2. Shew that cos. (A — B) = cos. A cos. B + sin. A sin. B. 3. Shew...

...Dividing equation (1) by equation (2), member by member, we have, MM 10m n = i^or, m — n = logjr: hence, The logarithm of the quotient of two numbers, is equal to the logarithm of the dividend diminished by the logarithm of the divisor. 5. Since the logarithm of 10 is 1, the logarithm of the...

...equation (1) by equation (2), member by member, we have, mn MM 10 -=_r~0r, ra — tt = log-r^: hence, The logarithm of . the quotient of two numbers, is equal to the logarithm of the dividend diminished by the logarithm of the divisor. 5. Since the logarithm of 10 is 1, the logarithm of the...