 | Joseph Allen Galbraith - 1852 - 84 pages
...former of these equations by the latter N__ therefore N log -=n-ra = logAT-log M. M PROPOSITION П. The logarithm of the quotient of two numbers is equal to the difference of the logarithms of the numbers. If we raise each side of the equation , N=1on to the power... | |
 | Education - 1852 - 512 pages
...term of the expansion of (fl8 + ^)\ SECTION IV. — 1. Define the logarithm of a number, and show that the logarithm of the quotient of two numbers is equal to the difference of their logarithms. 2. Show that Cos (A — B) = Cos A Cos B + Sin A Sin B. 3. Show that... | |
 | Henry Law - Logarithms - 1853 - 84 pages
...or, the sum of the logarithms of m and n is the logarithm of their product. PROPOSITION N. THEOREM. The logarithm of the quotient of two numbers is equal to the logarithm of the dividend, with the logarithm of the divisor subtracted from it. Let X and / denote the same as in the foregoing... | |
 | Sir James Kay-Shuttleworth - Church and education - 1853 - 522 pages
...determine the middle term of the expansion of Section 4. 1. Define the logarithm of a number, and show that the logarithm of the quotient of two numbers is equal to the difference of their logarithms. 2. Show that Cos (A- 13) = Cos A Cos B + Sin A Sin B. 3. Show that... | |
 | Charles Davies - Navigation - 1854 - 446 pages
...Dividing equation (1) by equation (2), member by member, we have, 10m~n = -^or, m — n~logj^: 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, the logarithm of the... | |
 | Charles Davies - Geometry - 1854 - 436 pages
...Dividing equation (1) by equation (2), member by member, we have, JO™ »BB_OTjW_Wesi0g— : 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, the logarithm of the... | |
 | Charles Davies, William Guy Peck - Mathematics - 1855 - 628 pages
...the factors, taken separately. 2. The logarithm of the quotient of one number by another, is ci/ual to the logarithm of the dividend, minus the logarithm of the divisor. 3. The logarithm of any power oj a. quantity, is equal to the product of the logarithm of the quantity... | |
 | Adrien Marie Legendre, Charles Davies - Geometry - 1857 - 442 pages
...equation (1) by 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 of the... | |
 | Charles Davies - Algebra - 1857 - 408 pages
...I -— 1 ; that is, The logarithm of the quotient which arises from dividing one number by another is equal to the logarithm of the dividend minus the logarithm of the divisor. 232i If we raise both members of equation (1) to the «'* power, we have, a*.' = N'n (5). But from... | |
 | James B. Dodd - Algebra - 1859 - 368 pages
...have y=nm (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...of the dividend minus the logarithm of the divisor. Dividing the Equation ax = n by the Equation av=m, we have az-v=n-^m (47), i in which x — y is the... | |
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The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor. , M , ,• , . logi — = log 
