| Horatio Nelson Robinson - Algebra - 1864 - 444 pages
...have mr = an; therefore, log. (mr) = rx = r log. m. 6. — The logarithm of any root of a number ù **equal to the logarithm of the number divided by the index of the root.** For, let то = a1 ; then x = log. от. • By evolution we have \Ara = <f ', x log. m therefore,... | |
| Lefébure de Fourcy (M., Louis Etienne) - Trigonometry - 1868 - 346 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,... | |
| Edward Brooks - Geometry - 1868 - 294 pages
...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 logarithm of 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... | |
| Adrien Marie Legendre - Geometry - 1871 - 492 pages
...have, 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 at1ons of multiplication and division, by... | |
| Charles Davies - Surveying - 1871 - 458 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,... | |
| 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 - 318 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 =... | |
| Adrien Marie Legendre - Geometry - 1874 - 512 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... | |
| Mechanical engineering - 1874 - 1182 pages
...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... | |
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