 | Charles William Hackley - Algebra - 1847 - 546 pages
....-. by definition, x — x" is the logarithm of ^ ; that is to say, The logarithm of a fraction, or of the quotient of two numbers, is equal to the logarithm of the numerator minus the logarithm of the denominator. III. Raise both members of equation (1) to the nth... | |
 | 1852 - 316 pages
...of the expansion of HJ (« + 4 )». SECT. 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. Shew that cos. (A — B) = cos. A cos. B + sin. A sin. B. 3. Shew... | |
 | Adrien Marie Legendre - Geometry - 1852 - 436 pages
...Dividing equation (1) by equation (2), member by member, we have, mn MM 10 -=_r~0r, ra — tt = log-r^: hence, The logarithm of . the quotient of two numbers,...any .number by 10, will , be greater by 1 than the logarithm of that number ; also, the logarithm of the quotient of any number divided by 10, will be... | |
 | Charles Davies - Navigation - 1852 - 412 pages
...Dividing equation (1) by equation (2), member by member, we have, MM 10m n = i^or, m — n = logjr: hence, The logarithm of the quotient of two numbers,...the product of any number by 10, will be greater by I than the logarithm of that number; also, the logarithm of the quotient of any number divided by 10,... | |
 | 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... | |
 | Charles Davies - Geometry - 1886 - 340 pages
...equation (1) by equation (2), member by member, we have " ,m— n M ' M 10 = — or, m- — n = log -j^-: hence, The logarithm, of the quotient of two numbers, is equal to Iht logarithm of the dividend diminished by the logarithm of tho divisorOf Logar1thms. 4. Since the... | |
 | 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... | |
 | 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
...product. 4. 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,...of any number by 10, will be greater by 1 than the logarithm of that number; also, the logarithm of the quotient of any number divided by 10, will be... | |
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The logarithm of . the quotient of two numbers, is equal to the logarithm of the dividend diminished by the logarithm of the divisor. 
