| Colin MacLaurin - Calculus - 1801
...art. 728) +-+- + &c. This likewise follows from the property of logarithms, that the logarithm of the **product is equal to the sum of the logarithms of the factors;** and consequently the fluxion of the logarithm ofp equal to the sum <>f the fluxions of the logarithms... | |
| Charles Tayler, Leonhard Euler - 1824
...shall resume pur former equation, viz. log. be = log. b + log. c, which comprehends the property that **the logarithm of a product is equal to the sum of the logarithms of the factors.** First, as log. 2 = x, and log. 10 = 1, we have log. 20 = ^+1 log. 200 = ^ + 2 log. 2000 = ^+3 log.... | |
| William Smyth - Algebra - 1830 - 264 pages
...by member, we have yy' y" = a*+x'+x" whence. log y y'y"=* + x' + x"= log y + log y'+ logy" That is, **the logarithm of a product is equal to the sum of the logarithms of the factors** of this product. If then a multiplication be proposed, we take from a table of logarithms the logarithms... | |
| Bourdon (M., Louis Pierre Marie) - Algebra - 1831 - 389 pages
...the rule for the exponents (No. 180), we find yyy"y"' .... ^a'+*+J"+»"+' • • • Hence thai is, **the logarithm of a product is equal to the sum of the logarithms of the factors** of this product. Secondly. Suppose it is required to divide y by y', and let x and x' represent their... | |
| William Smyth - Algebra - 1836 - 280 pages
...= a^ + *' + «" whence log y y' y" ~= x -\- x' -f x" = log y -f~ log y' -\- log y' . That is, //i« **logarithm of a product is equal to the sum of the logarithms of** llie factors of this product. If then a mulplication be proposed, we take from a table of logarithms... | |
| Augustus De Morgan - Algebra - 1837 - 256 pages
...has its Logarithm between 0 and 1 1 and 2 2 and 3 Sec. 0 and —1 — 1 and —2 — 2 and —3 &c. **THEOREM V. The logarithm of a product is equal to...logarithms of the factors. Let a be the base, and** p, q, and r, the logarithms of P, Q, and K. Then P = a" Q = a" R = a' PQR = af+2+'• or log(PQR) =p... | |
| James Bryce - 1837
...known, its logarithm in another system may be found. 192. Schol. i. It follows, from Art. 35, 40, that **the logarithm of a product is equal to the sum of the logarithms of** its factors; and that the logarithm of a quotient is equal to the difference of the logarithms of the... | |
| John Hymers - Trigonometry - 1841 - 151 pages
...logep ; and as this process may be continued to any number of factor», we conclude, generally, that **the logarithm of a product is equal to the sum of the logarithms of** its factors. 8. The logarithm of a quotient is equal to the logarithm of the dividend diminished by... | |
| William Scott - Algebra - 1844 - 500 pages
...logarithms of yy'.y" ...; -„ y~, V~respcctively; whence, as has been already proved (Art. 208 — 211), **the logarithm of a product is equal to the sum of the logarithms of the factors** of that product ; the logarithm of a quotient is equal to the excess of the logarithm of the dividend... | |
| Ormsby MacKnight Mitchel - Algebra - 1845 - 294 pages
...a1 =n, ax'=n', ax+x'=nXn'. The product, nXn' has for its logarithm x-\-x'; or, the logarithm of any **product is equal to the sum of the logarithms of the factors** of the product. In case we wished to multiply any two numbers by logarithms, search in the tables for... | |
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