...logarithm is the sum of the 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...

...generally, that the logarithm of a product is equal to the sum of the logarithms of its factors. 8. The logarithm of a quotient is equal to the logarithm of the dividend diminished by that of the divisor. ч 102 Since m - o*, n — а", та* .-.-=— = а-', n а? •'•...

...the factors, taken separately. 2. The logarithm of the quotient of one number by another, is ci/ual to the logarithm of the dividend, minus the logarithm of the divisor. 3. The logarithm of any power oj a. quantity, is equal to the product of the logarithm of the quantity...

...I -— 1 ; that is, The logarithm of the quotient which arises from dividing one number by another is equal to the logarithm of the dividend minus the logarithm of the divisor. 232i If we raise both members of equation (1) to the «'* power, we have, a*.' = N'n (5). But from...

...generally, that the logarithm of any product is equal to the sum of the logarithms of its factors. 8. The logarithm of a quotient is equal to the logarithm of the dividend diminished by that of the divisor. Since m — a", n = a", m a_ i fm\ ii .'' S" (n) = X~y= g" m ~ g°...

...therefore m= a", n = d?; therefore m/n - aa* = a'+'; therefore log, mn - x + y = log. m + log„ n. 53G. The logarithm of a quotient is equal to the logarithm of the dividend diminished by the logarithm of the divisor. For let x — log. m, y = log. n ; therefore m = a', therefore...

...then and, by substituting these values in the last logarithmic equation, we have, considering that the logarithm of a quotient is equal to the logarithm...of the dividend minus the logarithm of the divisor, log. (»+i>- log. B=2ar(^+^^+-pL—5.+fa,. ;)or log (w+1)= log. w+2M(-Li + 3-^-j. -H This last equation...

...definition, j that is, The logarithm of the quotient which arises from dividing on' number by another is equal to the logarithm of the dividend minus the logarithm of the divisor. 232i If we raise both members of equation (1) to the n'* power, we have, a«' = N'a ..... (5). But...

...(N' \ -]yr)-> that is, The logarithm of the quotient which arises from dividing one number by another is equal to the logarithm of the dividend minus the logarithm of tin divisor. 232t If we raise both members of equation (1) to the nth power, we have, But from the...

...Multiplying equations, member by member, we have Therefore, log (MX N) =. x -\-y = log M+ log N. 10. The logarithm of a QUOTIENT is equal to the logarithm of the dividend diminished by tftat of the divisor. For, by Art. 9, we have M=a*, N=a". * Dividing the first equation...