 | Benjamin Greenleaf - 1861 - 638 páginas
...™ = (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 - 1863 - 504 páginas
...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 - 1863 - 432 páginas
...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 - 1863 - 464 páginas
...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... | |
 | Horatio Nelson Robinson - 1864 - 444 páginas
...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,... | |
 | Elias Loomis - 1864 - 386 páginas
...obtain I Nm=am ; therefore, according to the definition, — is the logarithm of Nm; hence PROPERTY IV. The logarithm of any root of a number is equal to the logorithm of that number divided by the index of the root. EXAMPLES. Ex. 1. Find the square root of... | |
 | Lefébure de Fourcy (M., Louis Etienne) - 1868 - 350 páginas
...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,... | |
 | Edward Brooks - 1868 - 284 páginas
...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... | |
 | James Hamblin Smith - 1869 - 412 páginas
...logarithm of the number and the index denoting the power. Let m = a*. Then mr = a" = r . log m. 374. 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.... | |
 | James Hamblin Smith - 1870 - 286 páginas
...proceed thus log 13 = 1-1139434 4 4-4557736 which is the logarithm of 28561, the number required. 147. 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.... | |
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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. 
