 The logarithm of any power, integral or fractional, of a number is equal to the product of the logarithm of the number by the index of the power. For let m = a"; therefore m' = (a")  Plane Trigonometry ... - Page 93by Isaac Todhunter - 1860Full view - About this book
 | Charles Broughton - Mathematics - 1814 - 148 pages
...of the perfect powers of numbers. As the power of any number was obtained by the mere multiplication of the logarithm of the number by the index of the power, and vice versa, the logarithm of the root was obtained by dividing the logarithm of the power by its... | |
 | Bourdon (M., Louis Pierre Marie) - Algebra - 1831 - 446 pages
...both members to the power n Therefore, \ogyZ = ~. x= -. log y ; that is, the logarithm of any pmcer of a number is equal to the product of the logarithm of the number, by the exponent of the pmcer. Take n — 1, as a particular case'; there will result\ogym=m. logy, an equation... | |
 | William Smyth - Algebra - 1833 - 288 pages
...power, we have amx — ytn whence the logarithm of yx= mx = m log y. That is, the logarithm of any power of a number is equal to the product of the logarithm of this number by the exponent of the power. To form any power whatever of a number by means of a table... | |
 | John Hymers - Logarithms - 1841 - 244 pages
....-.-=— = а-', n а? •'• 1оёа (г ) = Х - У = l°Sam - loS«n9. The logarithm of any power of a number is equal to the product of the logarithm of the number by the index of the power. Since m = a', .-. m' = (a')' « a", where r is any number whole or fractional, positive or negative.... | |
 | William Scott - Algebra - 1844 - 568 pages
...log. x=— n log. a. Consequently, log. or"= — n log. a. Whence the logarithm of any power whatever of a number is equal to the product of the logarithm of the number by the exponent of the power. 211. Let r= \/a, and therefore r"=a. Then, by Article 210, n log. r=log. a.... | |
 | J. Goodall, W. Hammond - 1848 - 390 pages
...multiplication is involution ; and division is the extraction of roots. 3rd. The logarithm of any power of a number is equal to the product of the logarithm of the number by the index of the power.—4th. The logarithm of the root of any quantity is equal to the logarithm of the quantity divided... | |
 | John William Colenso (bp. of Natal.) - 1851 - 148 pages
...= 0. fyi' (iii) Logm" = wlogm, or the logarithm of any power of a number is obtained by multiplying the logarithm of the number by the index of the power. For m" = (a*)" = a"*, and .-. log(»z") = nx = nlogm. As the index in (iii) may be either integral or fractional^... | |
 | William Smyth - Algebra - 1855 - 370 pages
...power, we have a^ = ym; ' whence the logarithm of ym = mx = m log y. That is, the logarithm of any power of a number is equal to the product of the logarithm of this number by the exponent of the power. To form any power whatever of a number by means of a table... | |
 | William Smyth - Algebra - 1856 - 264 pages
...7V T m . U • JV f whence the logarithm of N" = mz ==m log. N. That is, the logarithm of any power of a number is equal to the product of the logarithm of this number by the expo* nent of the power. •ogarithms, we multiply the logarithm of the proposed... | |
 | John Hymers - Logarithms - 1858 - 292 pages
...dividend diminished by that of the divisor. Since m = а*, я = cf, n 9. The logarithm of any power of a number is equal to the product of the logarithm of the number by the index of the power. Since m = (f, .'. mr = (a1)' = a", .-. log. (от*) = rx = r log. m, where r is any number whole or... | |
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