| John William Colenso (bp. of Natal.) - 1851 - 148 pages
...evn' . & to Hence log— = logl — logm = — logwi, since logl = 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... | |
| A. D. Stanley - 1854 - 416 pages
...M=bm, M" = bm" ; but if M" is the mnth power of the base b, mn is the logarithm of M". Therefore ¡lie logarithm of any power of a number is obtained by multiplying the logarithm of that number into the number denoting the power. 13. Finally, if M is a number whose logarithm is m,... | |
| Charles Auguste A. Briot - 1863 - 376 pages
...subtracting from the logarithm of the dividend that of the divisor ; a number is raised to a power by multiplying the logarithm of the number by the exponent of the power ; and lastly, the root of a number is extracted by dividing the logarithm of the number by the index of the... | |
| Daniel Barnard Hagar - Algebra - 1873 - 278 pages
...of 6.4 = 0.80618 Logarithm of 40.96 = 1.61286 408. Rule for Involution by Logarithms. — Multiply the logarithm, of the number by the exponent of the power, and find the number corresponding to the product— (Art. 402.) PJtOBLXXB. 1. Find the fourth power of... | |
| William Guy Peck - Conic sections - 1876 - 376 pages
...9.566390 log- 1 0.246682 = 1.7647, Ans. Other applications. 8. "We may raise a number to any power by multiplying the logarithm of the number, by the exponent of the power, and then finding the number that corresponds to the resulting logarithm. We may extract any root of a number... | |
| Benjamin Greenleaf - 1879 - 346 pages
...360), we have as the logarithm of the power 3.2376, whose corresponding number is 1728. RULE. Multiply the logarithm of the number by the exponent of the power, and find the number corresponding to the result. EXAMPLES. 2. Find the square or second power of 36. Ans.... | |
| Benjamin Greenleaf - Algebra - 1879 - 322 pages
...360), we have as the logarithm of the power 3.2376, whose corresponding number is 1728. RULE. Multiply the logarithm of the number by the exponent of the power, and find the number corresponding to the result. EXAMPLES. 2. Find the square or second power of 36. Ans.... | |
| James Mackean - 1881 - 510 pages
...p ~ = — = ax~". N By definition, Iog0 p = x - y — logeN - logaP. III. — The logarithm of the power of a number is obtained by multiplying the logarithm of the numbcr by the index of the power. Let logaTT = x, then N = a1. Raise both sides of this equation to... | |
| George Albert Wentworth - Trigonometry - 1882 - 232 pages
...Therefore, log — = a — b = log A — log B. J3 4. The logarithm of a power of a number is found by multiplying the logarithm of the number by the exponent of the power. For, A" = (10a)" = 10e". Therefore, log A* = an = n log a. 5. The logarithm of the root of a number... | |
| George Albert Wentworth, George Anthony Hill - Logarithms - 1883 - 186 pages
...Therefore, В 10* A log - = a - b = lo В A - log B. 4. The logarithm of a power of a number is found by multiplying the logarithm of the number by the exponent of the power. For, Therefore, An= (10«)» = 10«». log An = an = n log A . 5. The logarithm of the root of a number... | |
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