 | James Hamblin Smith - 1870 - 452 pàgines
...proceed thus, log 13= 1-1139434 4 4-4557736 which is the logarithm of 28561, the number required. 458. The logarithm of any root of a number is equal to the quotient arising from the division of the logarithm of the number by the number denoting the root.... | |
 | Adrien Marie Legendre - 1871 - 490 pàgines
...r, of both members of (4), we have, whence, by the definition, * = log ?Jm. - . . . ( 9.) That is, the logarithm of any root of a number is equal to...logarithm of the number divided by the index of the root. The preceding principles enable us to abbreviate the oper at1ons of multiplication and division, by... | |
 | Charles Davies - 1871 - 448 pàgines
...both members of (4), we have, 1CT = ym; whence, by the definition, I = log j/^. ...... (9.) That is, the logarithm of any root of a number, is equal to...logarithm of the number divided by the index of the root. The preceding principles enable ns to abbreviate the operations of multiplication and division of numbers,... | |
 | Elias Loomis - 1871 - 302 pàgines
...the seventh power of 0.8952. EVOLUTION BY LOGARITHMS. (15.) It is proved in Algebra, Art. 341, that the logarithm of any root of a number is equal to the logarithm of that number divided by the index of the root. Hence, to extract tfot -cot of a number by logarithms,... | |
 | Charles Davies - 1872 - 464 pàgines
...of both members of ( 4 ), we have, • «d' = \/m ; whence, by the definition, ~ .... (9.) That is, the logarithm of any root of a number is equal to...logarithm of the number divided by the index of the root. TABLE OB LOGARITHMS. 9. A TABLE OF LOGARITHMS, is a table containing a set of numbers and their logarithms,... | |
 | Charles Elsee - 1873 - 320 pàgines
...above proof be considered fractional ( = - J, we have also ^ = 7 1ов.». ic the logarithm of a root is equal to the logarithm of the number, divided by the index of the root. 161.— PROP. Logawi = Log,,™ x Logai. For let logb m = y, and log„ Ь = z, then m = Ъ", Ь =... | |
 | Adrien Marie Legendre - 1874 - 500 pàgines
...members of (4), we have, 10r = whence, by the definition, * = log 'Jm. ' • • • ( 9.) That is, the logarithm of any root of a number is equal to...logarithm of the number divided by the index of the root. The preceding principles enable us to abbreviate the oper ations of multiplication and division, by... | |
 | Charles Davies - 1874 - 464 pàgines
...of both members of ( 4 ), we have, whence, by the definition, " = log^ . • • • (9.) That is, the logarithm of any root of a number is equal to the logarithm of the number divided by t/1e index of tie root. TABLE OF LOGARITHMS. 9. A TABLE OF LOGARITHMS, is a table containing a set... | |
 | 1874 - 1186 pàgines
...have log. y* (or log. */ y) = — log. y ; that is to say, the logarithm of any root of a number ia equal to the logarithm of the number divided by the index of the root. From these two last results it is obvious that by means of a table of logarithms numbers may be raised... | |
 | Aaron Schuyler - 1875 - 284 pàgines
...cube of 8.07. Ans. 525.55. 5. Find the fifth power of .9. Am. .59047. I EVOLUTION BY LOGARITHMS. f 25. Proposition. The logarithm of any root of a number...the number divided by the index of the root. Let (1) b' = n; then, by def., log n = x. V(l) = (2) br =\/n; then, by def., log Vх n = — • r. — log... | |
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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. 
