| Charles William Hackley - Algebra - 1847 - 503 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
...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
...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 - 334 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
...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 - 444 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... | |
| |