 | Simon Newcomb - Algebra - 1882 - 302 pages
...negative infinity. 311. The use of logarithms is founded on the four following theorems. THEOREM VII. The logarithm of a product is equal to the sum of the logarithms of its factors. Proof. Let p and q be two factors, and suppose h = logjB, k = log?. Then... | |
 | Harvard University - 1882 - 336 pages
...distance of the second headland from the first. 6. Prove the formulae : 2 tan i September. 1. Prove that the logarithm of a product is equal to the sum of the logarithms of the factors. 2. In a system of logarithms of which the base is 9, what are the logarithms... | |
 | James Hamblin Smith - 1883 - 466 pages
...Involution Multiplication, . . . Evolution Division, as we shall show in the next four Articles. 455. 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"+'; :. log,mn=x + y = log.m + logan. Hence... | |
 | Education, Higher - 1882 - 498 pages
...and explain the reason why the tangent when determined from the cosine has two values. 3. Prove that the logarithm of a product is equal to the sum of the logarithms of its factors. 4. Shew that cot {0 + tan-1 (tans0)} = 2 cot 0. 5. Prove that sin 0 > d... | |
 | Edwin Pliny Seaver, George Augustus Walton - Algebra - 1882 - 308 pages
...logarithm of NN'. The reasoning would be similar if there were three or more factors instead of two. Hence The logarithm of a product is equal to the sum of the Num. Log. Num. Log. Num. Log. Num. Log. Num. Log. 1 2 3 4 5 6 7 8 9 10 0.0000 0.s010 0.4771 0.6021... | |
 | John Bascombe Lock - 1882 - 378 pages
...10 and log^ 1 0. 211. We give here a formal proof of the following propositions : To prove that (i) The logarithm of a product is equal to the sum of the logarithms of the factors. (ii) The logarithm of a quotient is equal to the difference of the logarithms... | |
 | Simon Newcomb - Trigonometry - 1882 - 372 pages
...of Logarithms, The following properties of logarithms are demonstrated in treatises on algebra. I. The logarithm of a product is equal to the sum of the logarithms of its factors. II. The logarithm of a quotient is found by subtracting the logarithm of... | |
 | Benjamin Greenleaf - 1883 - 344 pages
...over the characteristic., denotes that it only is negative, as the mantissa is always positive. 358. The logarithm of a product is equal to the sum of the logarithm of its factort. For, let m and n be any two numbers, x and y their respective logarithms, whose base is a.... | |
 | Simon Newcomb - Algebra - 1884 - 576 pages
...— approaches zero as its limit. Hence, VI. The logarithm of 0 is negative infinity. VII. THEOBEM. The logarithm of a product is equal to the sum of the logarithm's of its factors. Proof. Let p and q be two factors, and suppose h = log p, k = log q. Then... | |
 | Webster Wells - 1885 - 368 pages
...denote that it alone is negative, the mantissa being always positive. PROPERTIES OF LOGARITHMS. 342. The logarithm of a product is equal to the sum of the logarithms of its factors. Assume the equations , , . , 00. ; whence, by Art. 334, 10» = n ) (y =... | |
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The logarithm of a product is equal to the sum of the logarithms of its factors. 
