 | Horatio Nelson Robinson - Geometry - 1860 - 470 pages
...number by the index of the root, and the quotient will be the exponent of the required root. Hence, the logarithm of a root of a number is equal to the quotient obtained by dividing the logarithm of the number by the index of the root. Now, understanding... | |
 | Henry Lee Scott - History - 1861 - 674 pages
...the product of the logarithm of the number by the exponent of the power ; and the logarithm of any root of a number is equal to the logarithm of the number divided by the index of the root. These properties of logarithms greatly facilitate arithmetical operations. For if multiplication is... | |
 | Benjamin Greenleaf - Geometry - 1861 - 638 pages
...™ = (a*)~ = a** . Therefore, log (M m) = xm = (log M ) X m. 12. The logarithm of the ROOT of any number is equal to the logarithm of the number divided by the index of the root. For, let n be any number, and take the equation (Art. 9) 1 ,mt—\ x log Af Therefore, log WM ) = -=... | |
 | Benjamin Greenleaf - Geometry - 1862 - 518 pages
...have Mm = (a*)i" = a™ . ' Therefore, log (Mn) =xm= (log M) X m. 12. The logarithm of the ROOT of any number is equal to the logarithm of the number divided by the index of the root. For, let n be any number, and take the equation (Art. 9) Therefore, log 13. Hence, by means of logarithms,... | |
 | Benjamin Greenleaf - Geometry - 1863 - 504 pages
...have Mm = (a*)"1 = a™ . Therefore, log (Mm) = xm = (log M) X m. 12. The logarithm of the ROOT of any number is equal to the logarithm of the number divided by the index of the root. For, let n be any number, and take the equation (Art. 9) Therefore, log 13. Hence, by means of logarithms,... | |
 | Horatio Nelson Robinson - Algebra - 1863 - 432 pages
...have mr = a1*; 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 m = a* ; then x .— log. m. X The principal use of logarithms is to facilitate arithmetical... | |
 | Adrien Marie Legendre - Geometry - 1863 - 464 pages
...definition, * = logy^T • • • • (9.) That is, the logarithm of any root of a number is equal t& the logarithm of the number divided by the index of the root. TABLE OF LOGAEITHMS. 9. A TABLE OF LOGAEITHMS, is 'a table by means of which we can find the logarithm... | |
 | Benjamin Greenleaf - Algebra - 1864 - 420 pages
...rth power, we have mr = (<f)r = a*". Therefore, log (TO') = xr = r log m. 402. 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 m = a' ; then, extracting the rth root of both members, we have 403. The arithmetical mean... | |
 | 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 - 350 pages
...shall have 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,... | |
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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. 
