 | Benjamin Franklin Young - 1925 - 778 páginas
...3(0.47712) multiplied by 3 gives log 1.43136 which is the logarithm of 27, the cube of 3. 4. Roots — The logarithm of any root of a number is equal to...logarithm of the number divided by the index of the root. Specifically, we (i) find the logarithm of the number, (2) divide it by the index of the root, and... | |
 | Lloyd Leroy Smail - 1925 - 338 páginas
...logarithm of the number multiplied by the exponent of the power: log M" = n log M. IV. The logarithm of a root of a number is equal to the logarithm of the number divided by the index of the root: log \/M = - log M. n - ^ As an example of the detailed prtJof of these laws, let us consider the first.... | |
 | Ernst Rudolph Breslich - 1926 - 272 páginas
...extracting roots by logarithms is exceedingly simple. The following theorem is used : The logarithm of a root of a number is equal to the logarithm of the number divided by the index of the root, ie, . n— log a log-ya = — ^n To prove this let log a = m. Thena = 10 m . ». m .'.loga-=— n or... | |
 | George Gailey Chambers - 1925 - 280 páginas
...is also true for fractional and negative values of n. IV. The logarithm of a root of a number equals the logarithm of the number divided by the index of the root. Consider \/c and let c = kx or logic = x Then r .-. 1 xr/— 1 V c = Cr= kr or log* vc = In practice,... | |
 | Edward Ira Edgerton, Perry Amherst Carpenter - 1925 - 398 páginas
...power, (a?)" = am = Mn. Hence, log0 M " = xn = n • log0 M. 6. The logarithm of a root of a number is the logarithm of the number divided by the index of the root, or, stated in symbols, Loga -\/M = - loga M. n Proof: Let x = loga M , so that a* = M. Extracting the... | |
 | William Raymond Longley, Harry Brooks Marsh - 1926 - 608 páginas
...v/T88 = 0.9655 = i log 788 This example illustrates the following rule. Rule. The logarithm of the root of a number is equal to the logarithm of the number divided by the index of the root. General proof. IV. To prove : logb Vp = n Let P = b=, then log„P = x. Then Ур = \fa = b» . Hence,... | |
 | 1926 - 890 páginas
...affected by an exponent is equal to the exponent times the logarithm of the number. 4. The logarithm of a root of a number is equal to the logarithm of the number divided by the index of the root. For example, to multiply 50 by 70, log (70 X 50) = log 70 -flog 6 + log lO" = 1.8451 + 0.6990+1 = 3.5441... | |
 | Arthur McCracken Harding, George Walker Mullins - 1928 - 344 páginas
...multiplied by the logarithm of the number. For Mk = (a1)* = akx. Hence logo Mk = kx = k logo M. (10) The logarithm of any root of a number is equal to...logarithm of the number divided by the index of the root. For W = (a*)1/* = a*lk. Hence loga VM = xfk = r loga M . NOTE. While (6) is true, negative numbers... | |
 | 1940 - 414 páginas
...equal to the logarithm of the number multiplied by the exponent of the power. The logarithm of the root of a number is equal to the logarithm of the number divided by the index of the root. 5. Proportional parts. — Suppose it is required to find the logarithm of 2245.7. First find the mantissa... | |
 | Coast Artillery School (U.S.) - 1943 - 64 páginas
...is equal to the logarithm of the number multiplied by the exponent of the number. The logarithm of a root of a number is equal to the logarithm of the number divided by the index of the root. To find (13,000) 4: Log 13,000 = 4.11394; 4 X Log 13,000 = 16.45576; finding the antilog of 16.45576,... | |
| |
The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power. 
