 | Insurance - 1869 - 510 pages
...a nor b nor c will hold its usual place among the letters. — 13 QUESTIONS FOR 1866. J. Prove that the logarithm of a product is equal to the sum of the logarithms of the factors. In the common system of logarithms, what is the effect (1) of adding 1 to... | |
 | James Hamblin Smith - 1869 - 412 pages
...logarithm of m to the base a. In the four following Articles, we shall suppose the base to be a. 371. The logarithm of a product is equal to the sum of the logarithms of its factors. Let m = a', and n = a". Then mn = a'+s ; «'. log ти = x + y = log m +... | |
 | Carl Bruhns - Logarithms - 1870 - 646 pages
...log A + log В log -£- = log A — log В log Am = m log A log -pX = -i- log A, or at full length: 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 difference of the logarithms... | |
 | Benjamin Greenleaf - Algebra - 1871 - 412 pages
...real logarithm. For, since the base a is positive, all its powers must be positive (Art. 202). 399. The logarithm of a product is equal to the sum of the logarithms of its factors. For, let\ m = a", and n = a" ; then, multiplVing these equations, member... | |
 | Daniel Barnard Hagar - Algebra - 1873 - 278 pages
...logarithm of the product of two or more numbers is equal to the sum of the logarithms of those numbers. For, let m and n be any two numbers, x and y their respective logarithms, and a the base of the system. Then, by the definition of a logarithm, we have ax=m, a" = n. Multiplying... | |
 | Joseph Ficklin - Algebra - 1874 - 446 pages
...positive, a1 is positive, whether x is positive or negative. Thus, 10s = 100, and lO'2 = ^ = ~. 560. The logarithm of a product is equal to the sum of the logarithms of its factors. Let x = logam, and y = logen ; then m = af, and n — o?; whence, mn = axa«... | |
 | John Clement P. Aldous - 1874 - 104 pages
...aioKa*+iog.!/. (1) - X Dividing, a10*«" = - = y (2) î/ Raising to the power m, a10*«*"1 = xm = (3) 76 1. The logarithm, of a product is equal to the sum of the logarithms of the factors, as Iog106 = log103+log102. 2. The logarithm of a quotient is equal to the... | |
 | Benjamin Greenleaf - Trigonometry - 1876 - 204 pages
...the left of the unit»' place, and negative when on the right. GENERAL PROPERTIES OF LOGARITHMS. 9. The logarithm of a PRODUCT is equal to the sum of the logarithms of its factors. For let Л/ and ЖЪе any two numbers, x and y their respective logarithms,... | |
 | Benjamin Greenleaf - Algebra - 1879 - 350 pages
...over the characteristic, denotes that it only is negative, as the mantissa is always positive. 3581 The logarithm of a product is equal to the sum of the logarithm of its factors. For, let m and и be any two numbers, x and у their respective logarithms, whose base is a. Then, by Art. 349, we... | |
 | R. M. Milburn - Mathematics - 1880 - 116 pages
...101. loga oo = oo. 102. (i) loga mn=\ogam + logan; (ii) logamnr ---- =logaw+loga«+logar+ ---- ; or, the logarithm of a product is equal to the sum of the logarithms of its factors. 103. or, the logarithm of a quotient is equal to the logarithm of the dividend... | |
| |
The logarithm of a product is equal to the sum of the logarithms of its factors. 
