...any number of factors. Example. Iog10(79 x 642) = log,079 + log,0642. 114. Logarithm of a quotient. The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor. PROOF : As above, let logo« = x and logaV = y. Then ax = u, and...

...log 0.0001 = 0. 48. log 10,000 - log 1000 + log 100,000 - log 100 = 4. 40. Logarithm of a Product. The logarithm of the product of two numbers is equal to the к«т of the logaritJinis of the numbers. Let A and В be the numbers, and x and y their logarithms....

...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 =...

...must be 1, and the equation a = a1 means, in the language of logarithms, (4) log,, a = 1. THEOREM 3. The logarithm of the product of two numbers is equal to the sum of their logarithms, If yl and y2 be the numbers and xl and x2 their logarithms, the definition gives...

...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. To prove, log0 — = log0 m — log0 n. n Let log0 m = x then of...

...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...