| William Guy Peck - Algebra - 1875 - 348 pages
...have, aP* = mp; whence, by definition, px — Log mp; . . . . (7) hence, the following principle: 3°. **The logarithm of any power of a number is equal to...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, ^... | |
| Benjamin Peirce - 1875 - 306 pages
...Logarithm of Root, Quotient, and Rec'procal. that is, the logarithm of any power of a number is < >/>i<> / **to the logarithm of the number multiplied by the exponent of the power.** 12. Corollary. If we substitute p = m", or m— v//;, in the above equation, it becomes • log. p... | |
| Robert Potts - Arithmetic - 1876 - 392 pages
...eloe«« by def. Then raising each to the wlh power. a' = «"log««. .-. log„{«"} = » log.«. Or, **the logarithm of any power of a number, is equal to the** product of the logarithm of the number and the index of the power. 5. PB.OP. To find the logarithm... | |
| Benjamin Greenleaf - Trigonometry - 1876 - 204 pages
...member by member, we have .М_а^_ . N — a« Therefore, log f-^Л =x — y= log M — log Ж 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... | |
| Robert Potts - Arithmetic - 1876 - 418 pages
...«logc" by def. Then raising each to the »ih power. a• = a-dogi«. .•. loga{«•} = n loga«. Or, **the logarithm of any power of a number, is equal to the** product of the logarithm of the number and the index of the power. 5. PEOP. To find the logarithm of... | |
| Edward Brooks - Arithmetic - 1877 - 564 pages
...by the second, we have, »•— f Hence, log ( — J = m — n, or, = log M — log N. PRIN. 6. — **The logarithm of any power of a number is equal to...the number multiplied by the exponent of the power.** For, since if we raise both members to the nth power, we have, 10 mn _ M * f Hence, log M" = mn, or,... | |
| Benjamin Greenleaf - Algebra - 1879 - 376 pages
...equations, ax = m, a" = n, and dividing, member by member, we have , „ in ax~>> — — n (V »/' 3fiO. **The logarithm of any power of a number is equal to...the number, multiplied by the exponent of the power.** For, assume the equation, a* = m, and raising both members to the power p, we have in which xp —... | |
| Benjamin Greenleaf - 1879 - 346 pages
...equations, a* = wi, ai — n, and dividing, member by member, we have in which x — y = loga ( —V 360. **The logarithm of any power of a number is equal to...the number, multiplied by the exponent of the power.** For, assume the equation, of =zm, and raising both members to the power p, we have <ff = mp, in which... | |
| Benjamin Greenleaf - Algebra - 1879 - 322 pages
...member, we have in which x — y = logn ( — Y 360. The logarithm of any power of a number is equnl **to the logarithm of the number, multiplied by the exponent of the power.** For, assume the equation, dc = m, and raising both members to the power p, we have ax" = mP, in which... | |
| Elias Loomis - Algebra - 1879 - 398 pages
...corresponding to the resulting logarithm, and it will be the quotient required. 398. Tlte logariOim **of any power of a number is equal to the logarithm of** that number multiplied by the exponent of the power. If we raise both members of Eq. (1) to any power... | |
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