| Ernest Julius Wilczynski - 1916 - 507 páginas
...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... | |
| Florian Cajori - 1916
...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... | |
| Florian Cajori - 1916
...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... | |
| George Neander Bauer, William Ellsworth Brooke - 1917 - 313 páginas
...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 =... | |
| Alfred Monroe Kenyon, William Vernon Lovitt - 1917 - 337 páginas
...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 —... | |
| Leonard Magruder Passano - 1918 - 144 páginas
...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... | |
| Leonard Magruder Passano - 1918 - 141 páginas
...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... | |
| ARTHUR SULLIVAN GALE, CHARLES WILLIAM WATKEYS - 1920
...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?,... | |
| Warren Clarence Young - 1962 - 91 páginas
...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... | |
| Jack L. Keyes - 1990 - 239 páginas
...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... | |
| |