| Benedict Sestini - Algebra - 1857 - 258 pages
...or a*-* = - ; a* vv a" z z and consequently, x — y = I.-, that is, The logarithm of the quotient **is equal to the logarithm of the numerator, minus the logarithm of the denominator.** Raise to the exponent c both members of the equation a*= z, we will have (a 1 )' = z° or a" = z°,... | |
| Adrien Marie Legendre - Geometry - 1857 - 444 pages
...equation (2), member by member, we have, , , Jf J/ 10m~" = .^or, m — n = log.r^: hence, The logarithm **of the quotient of two numbers, is equal to the logarithm of the** dividend diminished by the logarithm of the divisor. 5. Since the logarithm of 10 is 1, tf'e logarithm... | |
| William Smyth - Algebra - 1858 - 344 pages
...therefore by adding the logarithm of 5 to that of 7. Since moreover the logarithm of a fraction will be **equal to the logarithm of the numerator minus the logarithm of the denominator,** it will be sufficient to place in the tables the logarithms of entire numbers. 201. Below we have a... | |
| James B. Dodd - Algebra - 1859 - 368 pages
...(41), in which x-\-y is the logarithm of the product n m. Logarithm of a Quotient. (309.) The logarithm **of the quotient of two numbers, is equal to the logarithm of the** dividend minus the logarithm of the divisor. Dividing the Equation ax = n by the Equation av=m, we... | |
| Charles William Hackley - Algebra - 1864 - 530 pages
...that is to say, The logarithm of a fraction, or of the quotient of two numbers, is equal to tht • **logarithm of the numerator minus the logarithm of...denominator. III. Raise both members of equation (1) to the** nth power. N"=o". .-. by definition, nx is the logarithm of № ; that is to say, The logarithm of... | |
| Joseph Ray - Algebra - 1852 - 420 pages
...to a form in which it shall also be divisible by the same factor. Since the logarithm of a fraction **is equal to the logarithm of the numerator, minus the logarithm of the denominator** (Art. 361), therefore, . log. (l+x)- log. (l+z)= log. ( 1±? ) . But, by division, we find 'x=l-\-xz... | |
| Elias Loomis - Algebra - 1868 - 386 pages
...number corresponding to the resulting logarithm, and it will be the product required. 397. The logarithm **of the quotient of two numbers is equal to the logarithm of the** dividend diminished by that of the divisor. If we divide Eq. (1) by Eq. (2), member by member, we shall... | |
| Aaron Schuyler - Measurement - 1864 - 506 pages
...product of 85, .097, and .125. Ans. 1.03062. DIVISION BY LOGARITHMS. 16. Proposition. The logarithm **of the quotient of two numbers is equal to the logarithm of the** dividend minus the logarithm of the divisor. (" (1) 6-= yn; then, by def., log TO = x. Let ] ( (2)... | |
| Daniel Barnard Hagar - Algebra - 1873 - 278 pages
...member by member, we have ax+'=mn, in which x+y is the logarithm of the product mn. 4. The logarithm **of the quotient of two numbers is equal to the logarithm of the** dividend diminished by that of the divisor. For, dividing the equation a? = m by the equation a" =... | |
| Aaron Schuyler - Measurement - 1875 - 276 pages
...product of 85, .097, and .125. Ans. 1.03062. DIVISION BY LOGARITHMS. 16. Proposition. The logarithm **of the quotient of two numbers is equal to the logarithm of the** dividend minus the logarithm of the divisor. Г (1) b" = m; then, by def., log m = x. Let i. (_ (2)... | |
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