| Charles Tayler - 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... | |
| William Smyth - 1830 - 264 páginas
...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... | |
| Bourdon (M., Louis Pierre Marie) - 1831 - 389 páginas
...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... | |
| William Smyth - 1836 - 280 páginas
...= 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... | |
| James Bryce - 1837 - 80 páginas
...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 dividend and... | |
| Augustus De Morgan - 1837 - 248 páginas
...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 P = a" Q = a"... | |
| Augustus De Morgan - 1837 - 248 páginas
...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 P = a" Q = a'... | |
| John Hymers - 1841 - 151 páginas
...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 that of the... | |
| William Scott - 1844 - 500 páginas
...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... | |
| J. Goodall, W. Hammond - 1848
...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 number corresponding to the... | |
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