 | George Wentworth, David Eugene Smith - Trigonometry - 1915 - 388 pages
...so on for any number of factors. 41. Logarithm of a Quotient. The logarithm of the quotient of tico numbers is equal to the logarithm of the dividend minus the logarithm of the divisor. For if A = 10*, and В = 10r, then 4 = 10г~'i В and therefore log — = x — y В = log Л — log... | |
 | Henry Lewis Rietz, Arthur Robert Crathorne, Edson Homer Taylor - Algebra - 1915 - 266 pages
...Example. Iog10(79 x 642) = log,079 + log,0642. 114. Logarithm of a quotient. The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor. PROOF : As above, let logo« = x and logaV = y. Then ax = u, and av = v, and - = ax~v. v Hence, loga-... | |
 | Claude Irwin Palmer, Charles Wilbur Leigh - Logarithms - 1916 - 348 pages
...colog N = log •— = log 1 — log N. M 1 Also log -jy = log M + log д= = log M + colog N, that is: The logarithm of the quotient of two numbers is equal to the logarithm of the dividend plus the cologarithm of the divisor. To find the cologarithm of a number, subtract the logarithm of... | |
 | Ernest Julius Wilczynski - Algebra - 1916 - 542 pages
...x + y = Iog0 M + logo N, *. and this equation proves the theorem. VIII. The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor. PROOF. Using the same notations as in the proof of VII, we find and therefore logo — = x — y =... | |
 | Florian Cajori, Letitia Rebekah Odell - Algebra - 1916 - 238 pages
...We proceed to establish two other theorems that are no less fundamental. The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor. The proof is similar to that of the first theorem. Let J^and ^ be any two positive numbers. Let also... | |
 | Florian Cajori - 1916 - 236 pages
...We proceed to establish two other theorems that are no less fundamental. The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor. The proof is similar to that of the first theorem. Let N and NI be any two positive numbers. Let also... | |
 | Ernst Rudolph Breslich - Logarithms - 1917 - 408 pages
....=am-n Why? M = m and loga N = n • Then M = am and N =an M N' lOSa(^)=mn Why? = logaAf— loga N Hence the logarithm of the quotient of two numbers is equal...of the dividend minus the logarithm of the divisor. For example, log |- = log 8— log 3 EXEECISE Find log ^; log |-; log -fy*. 158. Logarithm of a power.... | |
 | George Neander Bauer, William Ellsworth Brooke - Trigonometry - 1917 - 346 pages
...This law enables us to replace multiplication by addition with the aid of a table of logarithms. (b) The logarithm of the quotient of two numbers is equal...of the dividend minus the logarithm of the divisor. From (1) and (2) above we have, applying a law of exponents, a''" = - or log. m-=xy nn ... loga —... | |
 | George Neander Bauer, William Ellsworth Brooke - Trigonometry - 1917 - 344 pages
...law enables us to replace multiplication by addition with the aid of a table of logarithms. (b) TJie logarithm of the quotient of two numbers is equal...of the dividend minus the logarithm of the divisor. From (1) and (2) above we have, applying a law of exponents, m -, m ax~" = — or log. — = x —... | |
 | Alfred Monroe Kenyon, William Vernon Lovitt - Mathematics - 1917 - 368 pages
...log;, M + Iog6 N. This can readily be extended to three or more factors. 4) The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor. For, — = _ = 6* it therefore log;,— = k — I = log;, M — log;, N. 5) The logarithm of the reciprocal... | |
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The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor. , M , ,• , . logi — = log 
