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" The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power. "
An Elementary Treatise on Algebra: To which are Added Exponential Equations ... - Page 262
by Benjamin Peirce - 1837 - 288 pages
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New University Algebra

Horatio Nelson Robinson - Algebra - 1875 - 430 pages
...= log. w. 771 By division, — = a" ; n therefore, log. I — ) = x — z = log. 7W — log. n. 5. The logarithm of any power of a number is equal to...the number multiplied by the exponent of the power. For, let m=cf; then z = log. m. By involution, m' = a" ; therefore, log. (mr) =rx = r log. m. 6. The...
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Elementary Treatise on Algebra

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...
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Elementary Arithmetic, with Brief Notices of Its History...

Robert Potts - Arithmetic - 1876 - 412 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...
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Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - Trigonometry - 1876 - 208 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...
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Elementary Arithmetic: With Brief Notices of Its History, Volumes 1-12

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...
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The Normal Higher Arithmetic: Designed for Common Schools, High Schools ...

Edward Brooks - Arithmetic - 1877 - 560 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,...
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New Elementary Algebra: Designed for the Use of High Schools and Academies

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 —...
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New Elementary Algebra

Benjamin Greenleaf - 1879 - 348 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...
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New Elementary Algebra: Designed for the Use of High Schools and Academies

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...
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A Treatise on Algebra

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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