| Charles Tayler - 1824 - 350 pages
...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 =... | |
| William Smyth - Algebra - 1830 - 278 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... | |
| Bourdon (M., Louis Pierre Marie) - Algebra - 1831 - 446 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... | |
| James Bryce - Algebra - 1837 - 322 pages
...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... | |
| Augustus De Morgan - Algebra - 1837 - 308 pages
...number, lie between am and a" ; then x, the logarithm, lies between m and n (see page 89). THEOREM V. The logarithm of a product is equal to the sum of the logarithms of the factors. Let a be the base, and;?, q, and r, the logarithms of P, Q, and 11. Then... | |
| Augustus De Morgan - Algebra - 1837 - 308 pages
...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 the sum of the logarithms of the factors. Let a be the base, and p, q, and r, the logarithms of P, Q, and K. Then... | |
| John Hymers - Logarithms - 1841 - 244 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... | |
| William Scott - Algebra - 1844 - 568 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... | |
| J. Goodall, W. Hammond - 1848 - 390 pages
...quantity less than 1. The properties of logarithms of greatest practical utility in calculation are—1st. The logarithm of a product is equal to the sum of the logarithms of its factors; so that to multiply numbers we have only to add their logarithms and the... | |
| William Smyth - Algebra - 1851 - 272 pages
...Nt x -f- x' -\- x" will be the logarithm of NN'N". In all cases, therefore, we have this principle : The logarithm of a product is equal to the sum of the logarithms of the factors of this product. A multiplication then being proposed, if we take from the... | |
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