 | Edward Albert Bowser - Algebra - 1888 - 868 pages
...log m ; then m = a*. Therefore m" = (a1)" = a** ; whence by definition, log mp = px = p log m. (7) The logarithm of any root of a number is equal to the logarithm of the number divided by the index of the root. For let x = log m ; then m = a1. 1 1 X Therefore m? = (a*)~r = ar ; whence by definition,... | |
 | Edward Brooks - Algebra - 1888 - 344 pages
...nth power, B"XIll = AT". Whence, log Jl/" = nxm. Or log M" = nx log if. PRIN. 6. The logarithm of the root of a number is equal to the logarithm of the number divided by the index of the root. For, let m = log M. Then, . B™ = M. Taking nth root, E* = M *. Whence, logJHA=-.... | |
 | George Albert Wentworth - Arithmetic - 1888 - 392 pages
...x 0.4771 = 5.2481. 413. As logarithms are simply exponents, therefore (§ 381), The logarithm of a root of a number is equal to the logarithm of the number multiplied by the index of the root. Thus, log 2* = Joflog2 = Jx0.3010 = 0.0753. log .002* = J of (7.3010... | |
 | Charles Davies - Algebra - 1889 - 330 pages
...root of both members of ( 3 ), denoted by r, we have, Whence, by definition, * = Log ym . . . . (S.) That is, the logarithm of any root of a number is...equal to the logarithm of the number divided by the index of the root. The applications of the above principles require a table of logarithms. A TABLK... | |
 | William Findlay Shunk - Railroad engineering - 1890 - 360 pages
...power of a number is equal to the logarithm of the number multiplied by the exponent of the power. The logarithm of any root of a number is equal to the logarithm of the number divided by the index of the root. 6. The preceding principles enable us to abridge labor in arithmetical calculations,... | |
 | William Joseph Hussey - Logarithms - 1891 - 172 pages
...any power of a number is equal to the logarithm of the number multiplied by the index of the power. The logarithm of any root of a number is equal to the logarithm of the number divided by the index of the root. Or, expressed in formulas, log ¿ X .B = log ¿ + logB, log = logA-logB, log A-... | |
 | William Joseph Hussey - Logarithms - 1891 - 178 pages
...number is equal to the logarithm of the number multiplied by the index of the power. The logari(hm of any root of a number is equal to the logarithm of the number div1ded by the index of the root. Or, expressed in formulas, log Л X .B = log A + log Я, log^ =logA—... | |
 | Henry Hunt Ludlow - Logarithms - 1891 - 322 pages
...logarithm of the number multiplied by the exponent of the power. 4°. The logarithm of any root of any number is equal to the logarithm of the number divided by the index of the root. Applications. 5. When the mantissa of a subtrahend is greater than that of the minuend,... | |
 | Edward Albert Bowser - Trigonometry - 1892 - 392 pages
...number multiplied by the exponent of the power. For let a; = log„m. .-. m = az. .-. logamp = px= (7) The logarithm of any root of a number is equal to the logarithm of the number divided by the index of the root. For let a;=logam. .-. m = a*. I » .-. mг = aг. - x I .: log(mг) = - = -logam.... | |
 | Edward Albert Bowser - Logarithms - 1908 - 128 pages
...power of a number is equal to the logarithm of the number multiplied by the exponent of the power. The logarithm of any root of a number is equal to the logarithm of the number divided by the index of the root. For the investigations of these rules the student is referred to the " Treatise... | |
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The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power. 
