...of logarithms, Iog0 (MN) = x + y = Iog0 M + logo N, *. and this equation proves the theorem. VIII. The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor. PROOF. Using the same notations as in the proof of VII, we find...

...Ni, L+L! = logarithm of N • N¡. Hence, the theorem, The logarithm of the product of two positive numbers is equal to the sum of the logarithms of the numbers. 112. The integral part of a logarithm is called its characteristic, and the decimal part is called...

...N1, L-\-Li = logarithm of N • Nv Hence, the theorem, TTie logarithm of the product of two positive numbers is equal to the sum of the logarithms of the numbers. 112. The integral part of a logarithm is called its characteristic, and the decimal part is called...

...illustrated is peculiar to the system of logarithms of which 10 is the base. 4. Laws of logarithms. (a) The logarithm of the product of two numbers is equal to the sum of the logarithms of the numbers. Given a* = m (1) or Iog0 m = x (3) a" = и (2) or loga n = y. (4) From the law of exponents ax+v =...

...whence Iog6 MN = k + I = log;, M + Iog6 N. This can readily be extended to three or more factors. 4) The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor. For, — = _ = 6* it therefore log;,— = k — I = log;, M —...

...theorem replaces the operation of multiplication by the simpler operation of addition. II. In any system the logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor. a* = m To prove, log.= n = log„ m — li Let log0m bg0 n = x...

...theorem replaces the operation of multiplication by the simpler operation of addition. II. In any system the logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor. To prove, log0 — = log0 m — log0 n. n Let log0 m = x then of...

...easily deduced from the corresponding properties of the exponential function as follows: 7. Theorem. The logarithm of the product of two numbers is equal to the sum of the logarithms of the numbers. Let p = bmj whence Iog6 p = m, and q = bn, whence log& q = n. Then pq = bmbn = bm+n. Therefore log?,...

...expressed, it is understood to be 10. Pages 60-64. The first property of logarithms given above states that the logarithm of the product of two numbers is equal to the sum of the logarithms of the two numbers. If you read these pages carefully, you will see that when you multiply two numbers using...

...the Henderson equation. First, take the logarithm of both sides of Equation 5-12, (5-13) J The log of the product of two numbers is equal to the sum of the logarithms of the two numbers, hence, (5-14) •[B-] " [B-] Substituting Equation 5-14 into 5-13, , L*"^J /C 1 C "\ multiplying...