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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 - 284 pages
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## An Algebra for Secondary Schools

Earle Raymond Hedrick - Algebra - 1908 - 442 pages
...logarithm of the dividend less that of the divisor, for 10m -=- 10" = 10m~". III. The logarithm of a power of a number is equal to the logarithm of the number multiplied by the exponent, of the power, for (10™)" = 10""'. This principle includes the extraction of roots by using fractional exponents,...
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## Elementary Algebra

Frederick Howland Somerville - Algebra - 1908 - 428 pages
...log m and y = log n. (Art. 438) Hence, in (3), log — = log m — log n. n i 455. The logarithm of a power of a number is equal to the logarithm of the number multiplied by the exponent of the power. Let 10" = m. (1) Raising both members of the equation to the pib power, 10** = m?. Whence, logmf=px....
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## Standard Algebra

William James Milne - Algebra - 1908 - 474 pages
...logarithms. Since logarithms are simply exponents, it follows that : 584. PRINCIPLE. — The logarithm of a power of a number is equal to the logarithm of the number multiplied by the index of the power; that is, To any base, log m" = n log m. For, let log„ m=x, and let n be any number,...
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## A Secondary Arithmetic

John Charles Stone - Business mathematics - 1908 - 268 pages
...a*-j. n Hence, loga -z = x — y = loga m — logo n. III. The logarithm ofapower of a number equals the logarithm of the number, multiplied by the exponent of the power For, let of — M. Then, nf = (a*)'" = af*. Hence, loga «'• = px = p loga n. IV. The logarithm of...
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## Plane Trigonometry

Levi Leonard Conant - Plane trigonometry - 1909 - 284 pages
...of the dividend minus the logarithm of the divisor. .'. log ~ — x — y — log m — log n. n 4. The logarithm of any power of a number is equal to the logarithm of the number multiplied by the index of the power. PROOF. mv = (10*)" = 10*y. .'. log mv = xy = y log m. 5. The logarithm of any root...
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## Plane and Spherical Trigonometry

Levi Leonard Conant - Trigonometry - 1909 - 316 pages
...logarithm of the dividend minus the logarithm of the divisor. PROOF. n .-.tog 2n = log m — log n. 4. The logarithm of any power of a number is equal to the logarithm of the number multiplied by the index of the power. PROOF. m? = (10*)" = 10*». .'. log m v = xy = y log m. 5. The logarithm of any...
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## Plane Trigonometry

Arthur Graham Hall, Fred Goodrich Frink - Plane trigonometry - 1909 - 276 pages
...log«, »— log«, m. (2) \Mfc/ Manifestly loga ( — )=» — loga m. \mJ III. The logarithm of the power of a number is equal to the logarithm of the number multiplied by the index of the power. For, if x = loga n, then n = ax. Hence, np = (a1)»1 = apx or, loga (n?) =px =...
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## Trigonometry

Arthur Graham Hall, Fred Goodrich Frink - Logarithms - 1909 - 264 pages
...x — y = loga n— loga m. (2) Manifestly loga ( . - ) = — loga m. \mj III. The logarithm of the power of a number is equal to the logarithm of the number multiplied by the index of the power. For, if x = loga n, then n = a*. Hence, np = (a1)" = ap* or, log« (n'») = px...
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## Practical Algebra (revised) Prepared for the Use of the Midshipmen at the ...

Stimson Joseph Brown, Paul Capron - Algebra - 1910 - 212 pages
...Using the same quantities as in III, we have 2L = b * = b xv nb* or logs f-^-j = logs m - logs n. V. The logarithm of any power of a number is equal to the logarithm of the number multiplied by the index of the power. Let m = b x , or logs m =• x; then m »= (6•)» = J~, or logs (mn) =nx. But...
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## Elements of Applied Mathematics

Herbert E. Cobb - Mathematics - 1911 - 298 pages
...logarithm of the divisor. III. log 2s = 3 log 2. 2» _ (100.8010)8 _ 1Q0.9080 _ g The logarithm of a power of a number is equal to the logarithm of the number multiplied by the exponent of the power. IV. log V3 = log 3* = J log 3. V3 = 3* = (10°-4771)* = 10°-2886 = 1.732. The logarithm of the root...
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