 | Benjamin Greenleaf - 1867 - 188 pages
...take the equation (Art. 9) M=ax, then, raising both sides to the with power, we have M m = (ax)m = a™ . Therefore, log ( Mm) =xm= (log M) X m. 12....let n be any number, and take the equation (Art. 9) M=a*, then, extracting the wth root of both sides, we have * Therefore, log 13. Hence, by means of... | |
 | Edward Brooks - Geometry - 1868 - 284 pages
...both members to the rath power, we have, 10"- = JM* Hence, log M n = mn, or, = log M X n. PRIN. 7. — The logarithm of the root of any number is equal to...the number divided by the index of the root. For, since 10" = M, if we take the nth root of both members, we have, Hence, log .\/~M= — , or, log 3f-f-... | |
 | Lefébure de Fourcy (M., Louis Etienne) - Trigonometry - 1868 - 350 pages
...a"» = <* УBut, ^ = log tj/"y7and x = log y. Hence «lo That is, the logarithm of the m"1 root of a number is equal to the logarithm of the number divided by the index of the root. LOQABITHlfS. 5 and then finding in the tables the number whoso logarithm is equal to the sum or difference,... | |
 | Charles Davies - Surveying - 1871 - 448 pages
...1CT = ym; whence, by the definition, I = log j/^. ...... (9.) 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 preceding principles enable ns to abbreviate the operations of multiplication and division of numbers,... | |
 | Charles Davies - Geometry - 1872 - 464 pages
...have, • «d' = \/m ; whence, by the definition, ~ .... (9.) 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. TABLE OB LOGARITHMS. 9. A TABLE OF LOGARITHMS, is a table containing a set of numbers and their logarithms,... | |
 | Horatio Nelson Robinson - Algebra - 1872 - 436 pages
...therefore, log. (mr) = rx = r log. m. 6. — The logarithm of any root of a number is equal to tkt logarithm of the number divided by the index of the root. For, let m = a* ; then x — log. m m By evolution we have Vm = «r J x log. m therefore. log. vm = — = •... | |
 | Aaron Schuyler - Measurement - 1864 - 506 pages
...power of .9. Ans. .59047. EVOLUTION BY LOGARITHMS. 25. Proposition. The logarithm of any root of a number is equal to the logarithm of the number divided by the index of the root. Let (1) b- = n; then, by def., log n = x. lX(l) = (2) b'r —1/n; then, by def., log 1</~^, = — .... | |
 | Charles Elsee - 1873 - 320 pages
...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 =... | |
 | Daniel Barnard Hagar - Algebra - 1873 - 278 pages
...ax = m to any power p, we have a?* = mP, in which xp is the logarithm of m raised to the power p. 6. The logarithm of the root of any number is equal to the logarithm of that number divided by the index of the root. For, extracting the rth root of both members of the equation... | |
 | Adrien Marie Legendre - Geometry - 1874 - 500 pages
...whence, by the definition, * = log 'Jm. ' • • • ( 9.) 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 preceding principles enable us to abbreviate the oper ations of multiplication and division, by... | |
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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. 
