| University of Oxford - 1879
...of a right-angled triangle, in which the perpendicular is 127 and the hypotenuse 325. 9. Prove that **the logarithm of the product of two numbers is equal to the sum of the logarithms of the numbers** themselves. Find A, when 10 tan^ = 7 sin 15° 30'. 10. In the triangle ABC, if B = 57° 45', C = 105°... | |
| Benjamin Greenleaf - 1879
...m, ai = n. Multiplying these equations, member by member, We have, in which, x 4- y = Ioga m n. 359. **The logarithm of a quotient is equal to the logarithm of the dividend** minus the logarithm of the divisor. For, assume the equations, a* = wi, ai — n, and dividing, member... | |
| Benjamin Greenleaf - 1879 - 336 páginas
...Multiplying these equations, member by member, We have, in which in which, x -\- y = loga m n. 359. **The logarithm of a quotient is equal to the logarithm of the dividend** minus the logarithm of the divisor. For, assume the equations, ax = m, a" = n, and dividing, member... | |
| R. M. Milburn - 1880 - 100 páginas
...---- ; or, the logarithm of a product is equal to the sum of the logarithms of its factors. 103. or, **the logarithm of a quotient is equal to the logarithm of the dividend** minus the logarithm of the divisor. 104. loga m"=n loga m; n being integral or fractional. _ i j. 105.... | |
| George Albert Wentworth - 1881 - 380 páginas
...following general proofs to the base a should be noticed. I. The logarithm of the product of two or more **numbers is equal to the sum of the logarithms of the numbers.** For, let m and n be two numbers, and x and y their logarithms. Then, by the definition of a logarithm,... | |
| Gaston Tissandier - 1882
...explanations are only wearying and unsatisfactory at best. The principle is, simply stated, the theorem that **the logarithm of the product of two numbers is equal to the sum of** their logs. The size of the dial will of course regulate the length of the calculation. The instrument... | |
| Edwin Pliny Seaver, George Augustus Walton - 1881 - 297 páginas
...Dividing, N-^-N' = b 1 -x' whence it appears (Art. 384) that x —x' is. the logarithm of N+N'. Hence **The logarithm of a quotient is equal to the logarithm of the dividend** less the logarithm of the divisor. 393- To find the logarithm of a power. Let N=lS. Taking the m lb... | |
| Henry Nathan Wheeler - 1882 - 43 páginas
...3 when the base is 10? Ans. 0.001. § 6. In any system the logarithm of the product of two or more **numbers is equal to the sum of the logarithms of the numbers.** Proof: If l = b", m = by, n = b', then is log6Z = x, Iog6m = 2/, logbn = z; now IX mxn = b* x Ъ»... | |
| Robert Hamilton Pinkerton - 1884 - 176 páginas
...calculated to 7 decimal places. 66. Properties of Logarithms. I. The logarithm of the product of two or 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... | |
| Charles Davies - 1889 - 320 páginas
...member, we have, a*+y — mrii Whence, from the definition, x + y = Log mn . . . . ( 5.) i That is, **the logarithm of the product of two numbers is equal to the sum of the logarithms of the** tiw numbers. If we divide ( 3 ) by ( 4 ), member by member, wo shall have, m a*-* — -• n Whence,... | |
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