...the colog N = log -^ = log 1 — log N. Ml Also log -^r = log M + log — = log M + colog N, that is: The logarithm of the quotient of two numbers is equal to the logarithm of the dividend plus the cologarithm of the divisor. The logarithm of the quotient of two...

...log ЛВС = log -a + logB + log C, and so on for any number of factors. 41. Logarithm of a Quotient. The logarithm of the quotient of two numbers is equal to the logarithm of the dividend minus the logarithm of the divisor. For if A = 10?, and В = 10», then —...

...colog N = log •— = log 1 — log N. M 1 Also log -jy = log M + log д= = log M + colog N, that is: The logarithm of the quotient of two numbers is equal to the logarithm of the dividend plus the cologarithm of the divisor. To find the cologarithm of a number,...

...This law enables us to replace multiplication by addition with the aid of a table of logarithms. (b) The logarithm of the quotient of two numbers is equal to the logarithm of the dividend minus the logarithm of the divisor. From (1) and (2) above we have, applying...

....=am-n Why? M = m and loga N = n • Then M = am and N =an M N' lOSa(^)=mn Why? = logaAf— loga N Hence the logarithm of the quotient of two numbers is equal to the logarithm of the dividend minus the logarithm of the divisor. For example, log |- = log 8— log 3...

...whence Iog6 q = n. Then pq = bmbn = 6m+n. Therefore log6 pq = m + n why? = log6 p + logi, q. 8. Theorem. The logarithm of the quotient of two numbers is equal to the logarithm of the dividend minus the logarithm of the divisor. Let p = bm and q = bn, whence log6 p...

...10x.10" = 10I + i' .-. log mn = x + y = log m + log n. Similarly log mnp = log m + log n + log p. Theorem II. — The logarithm of the quotient of two numbers...to the difference of the logarithms of the numbers. Let log m = x .-. m = lCP log n = yn=10» • ™-!2!=lOx-<" n 10" .•. log — ~xy = log m — log...

...at a time. Thus, the logarithm of a product is the sum of the logarithms of the several factors. (2) The logarithm of the quotient of two numbers is equal to the logarithm of the numerator minus the logarithm of the denominator. Let us use the same numbers as in...

...calculation: 1. The logarithm of a product is equal to the sum of the logarithms of its factors. 2. The logarithm of the quotient of two numbers is equal to the logarithm of the dividend less the logarithm of the divisor. 3. The logarithm of a number affected...

...extended to the product of any number of factors, thus log (mnp) = log m + log n + log p. 57. Theorem II. The logarithm of the quotient of two numbers is...to the difference of the logarithms of the numbers. Let logro = x .'. m = 10*, log n = y .'. n = 10", 10» = log т — log«. 58. Theorem III. The logarithm...