...logarithm of 2048 to the base 2 ? Since 2048 = 32-64, we have log¡ 2048 = log232 + log2 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, Iog6 (m -s- я) = log,, m - log,, я. Let log5 m = x and logb...

...and n = a" ; 3. and mn = ax • 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-...

...respectively equal to a, b and c, prove that — — -^=«. ao 10. Define a logarithm and prove that the logarithm of the product of two numbers is equal to the sum of their logarithms. Find the value of = • — . (3-721)"tf Given log 8-4=-9243, log 6'72='8274, log...

...it was not often taken. C. In TRIGONOMETRY the work was on the whole fairly good. Q. 33. Explain why the logarithm of the product of two numbers is * equal to the sum of the logarithms of the numbers. By means of logarithms given below, find the fifth root, and the fifth power of 0'69889 correct to...

...is evident that : The logarithm of a product is equal to the sum of the logarithms of the factors. The logarithm of a quotient is equal to the logarithm of the dividend less that of the divisor. The logarithm of a power of a number is equal to the logarithm of the number...

...(1) and (2), x = log m and y = log n. (Art. 438) Substituting in (3), log mn = log m + 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), jg = m....

...sum of the logarithms of its factors. Again, Therefore, loga ( — =xy = \ogam — loga n, n that is, the logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor. Thus Iog105 = Iog10 10 - log]02 = 1.0000 - 0.3010 = 0.6970. Raising...

...logarithm of a product is equal to the sum of the logarithms of the factors, for 10ra x 10" = 10"'+n. II. The. logarithm of a quotient is equal to the logarithm of the dividend less that of the divisor, for 10m -=- 10" = 10m~". III. The logarithm of a power of a number is equal...

...: logio 255 = logi0 3 + Iogi0 5 + Iogi0 17. BASE NUMBER 04 LOGARITHM 2 10 125 3 i 2 A 3 i 32 -5 2. The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor. As above, let lognм = x and lognv = y, then, a* = u, ay = v, and...

...numbers, and let x and y be their logarithms respectively. Then .'. log(ran) = x + y = log m + log n. 3. The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor. PROOF. n .-.tog 2n = log m — log n. 4. The logarithm of any power...