 | John Hymers - Logarithms - 1858 - 324 pages
...log„ (m') =rx = r log„ »»?, where r is any number whole or fractional, positive or negative. 10. The logarithm of the root of any number is equal to...logarithm of the number divided by the index of the root. Since m = a", .: log„ (Jm) = ^ = — (log.«»). 11. Hence, if we have to multiply two numbers together,... | |
 | Charles Davies - Algebra - 1860 - 412 pages
...=(N')"= yOF - - (6). But from the definition, — = log ("^W') ; that is, The logarithm of any root of a number is equal to the logarithm of the number divided by the index of the r.oot. 234( From the principles demonstrated in the four preceding articles, we deduce the following practical... | |
 | Henry Lee Scott - History - 1861 - 674 pages
...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
...M—cf, then, raising both sides to the with power, we have M ™ = (a*)~ = a** . Therefore, log (M m) = xm = (log M ) X m. 12. The logarithm of the ROOT of...let n be any number, and take the equation (Art. 9) 1 ,mt—\ x log Af Therefore, log WM ) = -= -fe— . 13. Hence, by means of logarithms, we can perform... | |
 | Benjamin Greenleaf - Geometry - 1862 - 532 pages
...the with power, we have Mm = (a*)m = a™ . Therefore, log (Mm) = xm = (log M ) X m12. The logariihm of the ROOT of any number is equal to the logarithm...let n be any number, and take the equation (Art. 9) Jf=rf', then, extracting the nth root of both sides, we have •=.. -\ - \ * log M - =3— Therefore,... | |
 | Benjamin Greenleaf - Geometry - 1863 - 502 pages
...sides to the rath power, we have M m = (a x ) m = a™ . Therefore, log (M m ) — xm = (log M) X ™. 12. The logarithm of the ROOT of any number is equal...number, and take the equation (Art. 9) Therefore, log (##) =%=^T' 13. Hence, by means of logarithms, we can perform multiplication by addition, and division... | |
 | 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 computations.... | |
 | 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
...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 of the logarithmt... | |
 | 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, loar. \/«i... | |
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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. 
