| Charles Davies, Adrien Marie Legendre - Geometry - 1869 - 470 pages
...that of the divisor. 7. Raising both members of (4) to the power denoted by p, we have, l01* = mp ; **whence, by the definition, xp = log mr ..... (8.)...root, indicated by r, of both members of (4), we have,** whence, by the definition, .... (9.) That is, the logarithm of any root of a number is equal to the... | |
| 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 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... | |
| 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 - 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";... | |
| 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.... | |
| Charles Davies - Leveling - 1871 - 448 pages
...of (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,...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...indicated by r, of both members of ( 4 ), we have,** • «d' = \/m ; whence, by the definition, ~ .... (9.) That is, the logarithm of any root of a number... | |
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