...2048 = 32 • 64, we have Iog22048 = Iog232 + Iog264 = 5 + 6 = 11. 7. The logarithm of и quotient is equal to the logarithm of the dividend minus the logarithm of the divisor; or, Iogb (m -=- я) = log„ m - log„ л. Let logb «n = x and logb n = y; then b" = m and &» =...

...numbers to a common base represent exponents of the same number, it follows that : 466. PRINCIPLE. — The logarithm of the quotient of two numbers is equal...of the dividend minus the logarithm of the divisor; that is, To any base, log (m ч- n) = log m — log n. The above principle may be established as follows:...

...exponents of the same number, it follows that: 466. PRINCIPLE. — The logarithm of the quotient oftivo numbers is equal to the logarithm of the dividend minus the logarithm of the divisor; that is, To any base, log (m -=- и) = log m — log n. The above principle may be established as follows:...

...2048 = 32 • 64, we have Iog2 2048 = logj 32 + logj 64 = 5 + 6 = 11 7. The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor; or, loge (m -r- n) = Iog6 m — log,, n. Let logj m = x and logb n = y; then Ъх = m and b* = n, and...

...Since 2048 = 32-64, we have log, 2048 = log, 32 + log, 64 = 5 + 6 = 11. 16. The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor; or, log» (m -i- n) = logt 14 — logu "• Let log» m = x and log» я = jr ; then b* = m and 6»...

...• ay = az+v. 4. .-. loga mn = x + y = loga m + loga n. 468. Prop. 4. The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor. 977 Dem. Let -- be the given quotient, m being the dividend 7Î- * » 1. For let x = log„rw and y...

...logarithm has a mantissa of .5150 ; .-. antilog of 1.5150 = 32.73 ; .'. 23. 12 X 1.416 = 32.73. (2) The logarithm of the quotient of two numbers is equal to the difference of the logarithms of the numerator and denominator or log a\b = log a - log b. Eg (i.) log...

...Hence loga(Jf x N) = x + y = IogaЛf+ logaJV. (ii) The logarithm of the quotient of two arithmetic numbers is equal to the logarithm of the dividend minus the logarithm of the divisor. Let Ж = a*, N=w1. Then M+N = a*-v. Hence loga(M- N) = x — y = logaM — \ogaN. (iii) The logarithm...

...Hence loga(Af x N) = x + y = logaJtf + logaN. (ii) The logarithm of the quotient of two arithmetic numbers is equal to the logarithm of the dividend minus the logarithm of the divisor. Let If = a«, N =a)i. Then Ж ч. N = a*- ». Hence loga (AT •*• N) = x — y = log«, Af - loga.2v"....

...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 by an exponent is equal to...