| James Bates Thomson - Algebra - 1878 - 324 pages
...numbers, m and n their logarithms, and b the base. Then 6»> = a And 6" = c Multiplying, &»+" = ae. 2°. **The logarithm of the dividend diminished by the logarithm of the divisor** is equal to the logarithm of the quotient of the two numbers. Let a and c denote any two numbers, m... | |
| James Bates Thomson, Elihu Thayer Quimby - Algebra - 1880 - 360 pages
...numbers, m and n their logarithms, and b the base. Then frm = a And 6" = e Multiplying, 6™+" = ae. 2°. **The logarithm of the dividend diminished by the logarithm of the divisor** is equal to the logarithm of the quotient. Let a and с denote any two numbers, m and n their logarithms,... | |
| Education, Higher - 1883
...the sum of two angles whose sines and cosines are given. 3. Prove that the logarithm of a quotient **is equal to the logarithm of the dividend diminished by the logarithm of the divisor.** 4. Find log '005957964, having given log 59579 = 4-7750933, log 59580 = 4"7751005. 5. Prove that in... | |
| James Hamblin Smith - 1883 - 444 pages
...treating of logarithms to the particular base 10, we may omit the suffix. 456. The logarithm of a quotient **is equal to the, logarithm of the dividend diminished by the logarithm of the divisor.** Let m=a', and n=a'. Then "ao"~'5 = log.m — log.n. Thus the operation of Division is changed into... | |
| Civil service commission - 1883
...ß aba / JS Sol. a + fl = • ' " «48 or + = + . QED 10. — Prove that the logarithm of a quotient **is equal to the logarithm of the dividend diminished by the logarithm of the divisor.** Given log. 2 = -69314718, log. 3 = 1-09861229 ; fiad the logarithms to base e of 8 /0\3e> /04 Д °/9"... | |
| Henry Law - 1884 - 582 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 I denote the same as in the foregoing... | |
| Robert Hamilton Pinkerton - Trigonometry - 1884 - 176 pages
...more numbers is equal to the sum of the logarithms of the numbers. II. The logarithm of a quotient **is equal to the logarithm of the dividend diminished by the logarithm of the divisor;** or (what is the same thing differently expressed) the logarithm of a fraction is equal to the logarithm... | |
| Eldred John Brooksmith, Robert Moir Milne - 1890 - 144 pages
...roots of the equation ax* + (a + b}x + b = o, . /3 a . b 10. Prove that the logarithm of a quotient **is equal to the logarithm of the dividend diminished by the logarithm of the divisor.** Given loge 2 = '69314718, log,. 3 = 1-09861229 ; find the logarithm to the base e of • (D 4-J (2)... | |
| Walter William Rouse Ball - Algebra - 1890 - 512 pages
...z + ... - loga m + loga n + \ogap + ... . 256. Logarithm of a Quotient. The logarithm of a quotient **is equal to the logarithm of the dividend diminished by the logarithm of the divisor.** Let m be the dividend, and let n be the divisor, and let n = a", .'. y = logan. m _ a* __ ry n a" =... | |
| Nathan Fellowes Dupuis - Algebra - 1892 - 362 pages
...a-- = a*-'. or bg/~ ) = Iog06 — logac. \e/ That is, the logarithm of the quotient of two numbers is **the logarithm of the dividend diminished by the logarithm of the divisor.** (3) (aI)" = &"=a'™. .-. log„(&n) = nx = nloga&. That is, the logarithm of the nth power of a number... | |
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