 | George Albert Wentworth - 1886 - 168 páginas
...Then m — ax, and mf = (az~)f = af*. .-, log mr = px, = p log m. LOGARITHM8. 277 IV. The logarithm cf the root of a number is equal to the logarithm of the number divided by the index of the root. For, let x bo the logarithm of m. Then m = a* and m* = (a*) = a*. 319. An exponential equation that... | |
 | Edward Brooks - 1888 - 344 páginas
...B» = M. Eaising to 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...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=-. 71 or k if *_!**;... | |
 | Edward Albert Bowser - 1888 - 868 páginas
...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, 1 x 1 log(m')... | |
 | Charles Ambrose Van Velzer, Charles Sumner Slichter - 1888 - 234 páginas
...Therefore, by definition, \og,,nf=pr That is, logan>=p log,,«. (c) 10. THEOREM. The logarithm of any root of a number is equal to the logarithm of the number divided by the index of the root. Let n be any number, and let loga n—x. Then, by definition, n=a* . Consequently v/«=a?. Therefore,... | |
 | George Albert Wentworth - 1888 - 392 páginas
...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 - 1889 - 330 páginas
...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 OF LOGARITHMS, is a... | |
 | James Morford Taylor - 1889 - 400 páginas
...the number multiplied by the exponent of the power ; and the logarithm of any root of a number equals the logarithm of the number divided by the index of the root. 307. From the principles proved above, we see that by the use of logarithms the operations of multiplication... | |
 | William Findlay Shunk - 1890 - 360 páginas
...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, by using simple... | |
 | William Joseph Hussey - 1891 - 172 páginas
...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- =n log Л, log i/2... | |
 | Henry Hunt Ludlow - 1891 - 322 páginas
...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, unity is added... | |
| |
The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power. 
