| Benjamin Greenleaf - 1869 - 516 pages
...member by member, we have Jf_£ --o.-». N -* o» Therefore, log I -^ I = x — y= log M — log N. 11. **The logarithm of any POWER of a number is equal to the** product of the logarithm of the number by the exponent of the power. For let m be any number, and take... | |
| James Hamblin Smith - 1869 - 412 pages
...diminished by the logarithm of the divisor. Let m = a', and и = a?, Then - = a"i; n m log m - log n, 373. **The logarithm of any power of a number is equal to the** product of the logarithm of the number and the index denoting the power. Let m = a*. Then mr = a" =... | |
| Benjamin Peirce - Algebra - 1870 - 302 pages
...all equal to each other, we have log. mmm &c. = log. m -j- log. m -j- log. m -j- &c. or log. mn = n **log. m ; Logarithm of Root, Quotient, and Reciprocal....the number multiplied by the exponent of the power.** 12. Corollary. If we substitute p = m", or in the above equation, it becomes n log. p = n log. v/ p,... | |
| Charles Davies - 1870 - 348 pages
...denoted by p, we have, pi p CL "~ Yfa • Whence, by definition, px — Log m? . . . ( 7.) That is, tJie **logarithm of any power of a number is equal to the...the number multiplied by the exponent of the power.** If we extract any root of both members of ( 3 ), denoted by r, we have, ar = Whence, by definition,... | |
| James Hamblin Smith - Algebra - 1870 - 452 pages
...1-7191323 their difference = -8508148 which is the logarithm of 7'092752, the quotient required. 457. **The logarithm of any power of a number is equal to the** product of the logarithm of the number and the index denoting the power. Let m—ax. Then mr=arx; =r.log«»i.... | |
| James Hamblin Smith - Trigonometry - 1870 - 286 pages
...1-7191323 their difference = -8508148 which is the logarithm of 7-092752, the quotient required. 146. **The logarithm of any power of a number is equal to the** product of the logarithm of the number and the index denoting the power. Let m = a'. Then m' = a";... | |
| Charles Davies - Surveying - 1871 - 458 pages
...(4), to a power denoted by t, we have, l0* = m'; whence, by the definition, pt = log m, ....... (8.) **That is, the logarithm of any power of a number, is...logarithm of the number multiplied by the exponent of** Ike power. 8. Extracting the root, indicated by r, of both members of (4), we have, 1CT = ym; whence,... | |
| Elias Loomis - Geometry - 1871 - 302 pages
...-0.4753 divided by -36.74. INVOLUTION BY LOGARITHMS. (14.) It is proved in Algebra, Art. 340, that **the logarithm of any power of a number is equal to the logarithm of** that number multiplied by the exponent of the power. Hence, to involve a number by logarithms, we have... | |
| Charles Davies - Algebra - 1871 - 404 pages
...the nih power, we have, a«*' = N/n ..... (5). But from the definition, we have, nxf = log (N'») ; **that is, The logarithm of any power of a number is equal to** tht logarithm of the number multiplied by the exponent of the power. 233. If we extract the nth root... | |
| Charles Davies - Geometry - 1872 - 464 pages
...denoted by p, we have, = m r whence, by the definition, xp = log m r ..... (8.) That is, the loga/ithm **of any power of a number is equal to the logarithm...the number multiplied by the exponent of the power.** 8. Extracting the root, indicated by r, of both members of ( 4 ), we have, • «d' = \/m ; whence,... | |
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