| Andrew Bell (writer on mathematics.) - 1839
...and x' = ly. And aх x aх = yy', or aх+х'=yy'; and hence x + x' = lyi/ or lytf = ly + ly'(502.) 1 **The logarithm of the quotient of two numbers is equal to the difference of** their logarithms.1 For ax -=- a* = - or e"' = -; and hence x — ж'= l ~, У У1 У' or l?L = ly —... | |
| William Chauvenet - 1843 - 92 páginas
...them together ; the sum will be found in the table to be the logarithm of the required product. 61. **The logarithm of the quotient of two numbers is equal to the difference of** their logarithms. For b and c being any two numbers, we have a\og.b—l) alog.<;_cDividing the first... | |
| 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 that if a, b,... | |
| 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 p, therefore PROPOSITION III. The logarithm... | |
| 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 if a, b, c be... | |
| Charles Davies - 1852 - 392 páginas
...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, is equal to the** logarithm of the dividend diminished by the logarithm of the divisor. 5. Since the logarithm of 10... | |
| Adrien Marie Legendre - 1852 - 432 páginas
...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, is equal to the** logarithm of the dividend diminished by the logarithm of the divisor. 5. Since the logarithm of 10... | |
| Sir James Kay-Shuttleworth - 1853 - 500 páginas
...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 if a, b, c be... | |
| Henry Law - 1853 - 68 páginas
...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... | |
| Charles Davies - 1854 - 322 páginas
...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... | |
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